DLMF: Untitled Document

… ►The full index form of an

m\times n

matrix

\mathbf{A}

is …

Bibliography M

… ►

Maple (commercial interactive system) Maplesoft.

ⓘ

Notes:: General purpose mathematical computing environment. Includes more than 100 special functions. Includes symbolic and arbitrary precision numerical computation.
Referenced by:: 1st item, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

… ►

Matlab (commercial interactive system) The MathWorks, Inc..

ⓘ

Notes:: General purpose mathematical computing environment. Includes a collection of special functions. Computations in double precision with symbolic and extended-precision capabilities available.
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

… ►

N. W. McLachlan (1947) Theory and Application of Mathieu Functions. Clarendon Press, Oxford.

ⓘ

Notes:: Corrected republication by Dover Publications, Inc., New York, 1964.
External Links:: MathReview (M. J. O. Strutt), ZentralBlatt
Referenced by:: §28.1, §28.2(i), §28.29(i), 1st item, 1st item, §28.33(ii), §28.4(vi), §28.4(vi), §28.5(i), §28.5(i), §28.9, Ch.28, Notations F, Notations G, Notations M, Notations N.
Encodings:: BibTeX

… ►

mpmath (free python library)

ⓘ

Notes:: Mpmath is a pure-Python library for multiprecision floating-point arithmetic. It provides an extensive set of transcendental functions, unlimited exponent sizes, complex numbers, interval arithmetic, numerical integration and differentiation, root-finding, linear algebra, and much more.
External Links:: mpmath
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

…

… ►This is also the normalization and notation of Chapter 33 for

Z=1

, and the notation of Weinberg (2013, Chapter 2). … ►Bound state solutions to the relativistic Dirac Equation, for this same problem of a single electron attracted by a nucleus with

Z

protons, involve Laguerre polynomials of fractional index. … ►, the J-matrix elements) as in Gautschi (1968), Golub and Welsch (1969), Gordon (1968). … ►

§18.39(iv) Coulomb–Pollaczek Polynomials and J-Matrix Methods

… ►with matrix eigenvalues

\epsilon=\epsilon^{N}_{i}

,

i=1,2,\dots,N

, and the eigenvectors,

\mathbf{c}(\epsilon)=(c_{0}(\epsilon),c_{1}(\epsilon),...,c_{N-1}(\epsilon))

, are determined by the recursion relation (18.39.46) below. …

… ►

SAGE (free interactive system)

ⓘ

Notes:: SAGE is a free open-source mathematics software system licensed under the GPL. It combines the power of many existing open-source packages into a common Python-based interface.
External Links:: Home Page
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

… ►

SLATEC (free Fortran library)

ⓘ

Notes:: The SLATEC Common Math Library is a large general purpose mathematical software library with broad coverage of elementary and special functions. Implementations in both single and double precision are provided. Developed by a consortium of US national laboratories. See Buzbee (1984).
External Links:: GAMS (package SLATEC)
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

… ►

Stembridge (website) John Stembridge’s Home Page

ⓘ

Notes:: Includes Maple software for zonal, Jack, and Macdonald polynomials; see the SF Package.
External Links:: Home Page
Referenced by:: § ‣ Software Cross Index.
Encodings:: BibTeX

… ►

G. W. Stewart (2001) Matrix Algorithms. Vol. 2: Eigensystems. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA.

ⓘ

External Links:: ISBN 0-89871-503-2, MathReview Entry, ZentralBlatt
Referenced by:: §3.2(vi).
Encodings:: BibTeX

… ►

J. A. Stratton, P. M. Morse, L. J. Chu, and R. A. Hutner (1941) Elliptic Cylinder and Spheroidal Wave Functions, Including Tables of Separation Constants and Coefficients. John Wiley and Sons, Inc., New York.

ⓘ

External Links:: MathReview (H. Bateman), ZentralBlatt
Referenced by:: §28.1, 7th item, Notations S, Notations S.
Encodings:: BibTeX

…

… ►

F. Calogero (1978) Asymptotic behaviour of the zeros of the (generalized) Laguerre polynomial

{L}_{n}^{\alpha}(x)

as the index

\alpha\rightarrow\infty

and limiting formula relating Laguerre polynomials of large index and large argument to Hermite polynomials. Lett. Nuovo Cimento (2) 23 (3), pp. 101–102.

ⓘ

External Links:: ISSN 0024-1318, Document, MathReview (R. A. Askey)
Referenced by:: §18.7(iii).
Encodings:: BibTeX

… ►

L. Carlitz (1960) Note on Nörlund’s polynomial

B_{n}^{(z)}

. Proc. Amer. Math. Soc. 11 (3), pp. 452–455.

ⓘ

External Links:: FullText, MathReview (M. P. Drazin), ZentralBlatt
Referenced by:: §26.1, §26.1, Notations S, Notations S.
Encodings:: BibTeX

… ►

CEPHES (free C library)

ⓘ

Notes:: This library treats about 180 different mathematical functions, including a substantial collection of probability integrals, Bessel functions, and higher transcendental functions. Implementations in single, double, and quad precisions are provided. See Moshier (1989).
External Links:: GAMS (package CEPHES)
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

… ►

CoStLy (free C-XSC library)

ⓘ

Notes:: Complex interval standard function library. For details see Neher (2007)
External Links:: CoStLy
Referenced by:: § ‣ Software Cross Index, M. Neher (2007).
Encodings:: BibTeX

… ►

A. Csótó and G. M. Hale (1997)

S

-matrix and

R

-matrix determination of the low-energy

{}^{5}\mathrm{He}

and

{}^{5}\mathrm{Li}

resonance parameters. Phys. Rev. C 55 (1), pp. 536–539.

ⓘ

External Links:: Document
Referenced by:: 2nd item.
Encodings:: BibTeX

…

… ►

Y. Ikebe, Y. Kikuchi, I. Fujishiro, N. Asai, K. Takanashi, and M. Harada (1993) The eigenvalue problem for infinite compact complex symmetric matrices with application to the numerical computation of complex zeros of

J_{0}(z)-iJ_{1}(z)

and of Bessel functions

J_{m}(z)

of any real order

m

. Linear Algebra Appl. 194, pp. 35–70.

ⓘ

External Links:: ISSN 0024-3795, Document, MathReview (Alan L. Andrew), ZentralBlatt
Referenced by:: §10.21(ix).
Encodings:: BibTeX

… ►

IMSL (commercial C, Fortran, and Java libraries) IMSL Nuerical Libraries..

ⓘ

Notes:: The IMSL Libraries are large general purpose numerical software libraries with broad coverage of elementary and special functions. Implementations are in single and double precision.
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

… ►

E. L. Ince (1940b) Further investigations into the periodic Lamé functions. Proc. Roy. Soc. Edinburgh 60, pp. 83–99.

ⓘ

External Links:: MathReview (H. Bateman), ZentralBlatt
Referenced by:: §29.1, §29.17(ii), §29.3(iii), §29.6(i), §29.6(ii), §29.6(iii), §29.6(iv), Ch.29, Notations E, Notations E, Notations E, Notations E.
Encodings:: BibTeX

… ►

M. E. H. Ismail and E. Koelink (2011) The

J

-matrix method. Adv. in Appl. Math. 46 (1-4), pp. 379–395.

ⓘ

External Links:: ISSN 0196-8858, Document, Link, MathReview (Boris Petrovich Osilenker)
Referenced by:: §18.39(iv).
Encodings:: BibTeX

►

M. E. H. Ismail, D. R. Masson, and M. Rahman (Eds.) (1997) Special Functions,

q

-Series and Related Topics. Fields Institute Communications, Vol. 14, American Mathematical Society, Providence, RI.

ⓘ

External Links:: ISBN 0-8218-0524-X, Document, Link, MathReview Entry, ZentralBlatt
Referenced by:: Profile Mourad E.H. Ismail.
Encodings:: BibTeX

…

… ►

G. H. Golub and C. F. Van Loan (1996) Matrix Computations. 3rd edition, Johns Hopkins University Press, Baltimore, MD.

ⓘ

External Links:: ISBN 0-8018-5413-X; 0-8018-5414-8, MathReview, ZentralBlatt
Referenced by:: §3.2(i), §3.2(i), §3.2(ii), §3.2(vii).
Encodings:: BibTeX

… ►

H. W. Gould (1960) Stirling number representation problems. Proc. Amer. Math. Soc. 11 (3), pp. 447–451.

ⓘ

External Links:: FullText, MathReview (L. Carlitz), ZentralBlatt
Referenced by:: §26.1, §26.1, Notations S, Notations S.
Encodings:: BibTeX

… ►

C. H. Greene, U. Fano, and G. Strinati (1979) General form of the quantum-defect theory. Phys. Rev. A 19 (4), pp. 1485–1509.

ⓘ

External Links:: Document
Referenced by:: item Greene et al. (1979):, Notations F, Notations F, Notations G.
Encodings:: BibTeX

… ►

K. I. Gross and D. St. P. Richards (1991) Hypergeometric functions on complex matrix space. Bull. Amer. Math. Soc. (N.S.) 24 (2), pp. 349–355.

ⓘ

External Links:: ISSN 0273-0979, Document, MathReview, ZentralBlatt
Referenced by:: §35.7(iii), §35.8(i), §35.8(ii), §35.8(iii), §35.8(iv).
Encodings:: BibTeX

… ►

GSL (free C library) GNU Scientific Library The GNU Project.

ⓘ

Notes:: The GNU Scientific Library is a large general purpose numerical software library with broad coverage of elementary and special functions. Implementation is in double precision.
External Links:: Home Page
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

…

… ►

T. Watanabe, M. Natori, and T. Oguni (Eds.) (1994) Mathematical Software for the P.C. and Work Stations – A Collection of Fortran 77 Programs. North-Holland Publishing Co., Amsterdam.

ⓘ

Notes:: Translated from the 1989 Japanese original. With 1 IBM-PC floppy disk (5.25 inch) containing a large general purpose mathematical software collection written in Fortran, including some special function codes. Double precision.
External Links:: ISBN 0-444-82000-0, MathReview, ZentralBlatt
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

… ►

G. Wei and B. E. Eichinger (1993) Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules. Ann. Inst. Statist. Math. 45 (3), pp. 467–475.

ⓘ

External Links:: ISSN 0020-3157, Document, MathReview (N. K. Thakare), ZentralBlatt
Referenced by:: §35.9.
Encodings:: BibTeX

… ►

E. T. Whittaker and G. N. Watson (1927) A Course of Modern Analysis. 4th edition, Cambridge University Press.

ⓘ

Notes:: Reprinted in 1996. Table errata: Math. Comp. v. 36 (1981), no. 153, p. 319.
External Links:: MathReview, ZentralBlatt
Referenced by:: §1.3(iii), §10.1, §12.11(i), §12.9(i), Ch.13, §15.6, Ch.15, Ch.19, §20.1, §20.1, §20.13, §20.2(i), §20.2(ii), §20.2(iii), §20.2(iv), §20.4(i), §20.4(ii), §20.5(ii), §20.7(ii), §20.7(iv), §20.7(viii), §20.9(i), §20.9(ii), §20.9(ii), Ch.20, §22.11, §22.13(i), §22.13(ii), §22.14(i), §22.14(iii), §22.14(iv), §22.15(i), §22.16(ii), §22.16(iii), §22.18(i), §22.18(iv), §22.2, §22.4(i), §22.4(ii), §22.4(iii), §22.5(i), §22.6(i), §22.6(iv), §22.7(i), §22.7(ii), §22.8(i), §22.8(ii), §22.8(iii), §22.8(iii), Ch.22, §23.1, §23.10(i), §23.2(ii), §23.2(iii), §23.22(ii), §23.3(i), §23.3(ii), §23.6(i), Ch.23, §24.1, Table 28.1.1, §29.12(iii), Ch.29, §31.8, §31.8, Ch.4, §5.11(i), §5.11(ii), §5.17, §5.8, (5.9.10_2), §5.9(i), §5.9(i), §5.9(ii), Ch.5, Notations K.
Encodings:: BibTeX

… ►

Wolfram’s Mathworld (website)

ⓘ

Notes:: A free resource from Wolfram Research built with Mathematica technology.
External Links:: Home Page
Referenced by:: 8th item, § ‣ Software Cross Index.
Encodings:: BibTeX

… ►

R. Wong and J.-M. Zhang (1994b) On the relative extrema of the Jacobi polynomials

P_{n}^{(0,-1)}(x)

. SIAM J. Math. Anal. 25 (2), pp. 776–811.

ⓘ

External Links:: ISSN 0036-1410, Document, MathReview (G. Gasper), ZentralBlatt
Referenced by:: §18.14(iii).
Encodings:: BibTeX

…

… ►

A. T. James (1964) Distributions of matrix variates and latent roots derived from normal samples. Ann. Math. Statist. 35 (2), pp. 475–501.

ⓘ

External Links:: FullText, MathReview (I. Olkin), ZentralBlatt
Referenced by:: §35.11, §35.4(i), §35.4(ii), §35.8(i), §35.8(ii), §35.8(iv), §35.9, Ch.35.
Encodings:: BibTeX

►

J. K. M. Jansen (1977) Simple-periodic and Non-periodic Lamé Functions. Mathematical Centre Tracts, No. 72, Mathematisch Centrum, Amsterdam.

ⓘ

External Links:: ISBN 90-6196-130-0, MathReview (V. P. Madan)
Referenced by:: §29.1, §29.1, §29.18(i), §29.19(i), §29.20(i), §29.20(i), §29.22(ii), §29.3(v), §29.6(i), §29.6(ii), §29.6(iii), §29.6(iv), Ch.29, Notations L, Notations L, Notations L, Notations L.
Encodings:: BibTeX

… ►

H. Jeffreys and B. S. Jeffreys (1956) Methods of Mathematical Physics. 3rd edition, Cambridge University Press, Cambridge.

ⓘ

Notes:: Reprinted in 1999.
External Links:: MathReview, ZentralBlatt
Referenced by:: §10.1, §12.17, Ch.14, Ch.6, §7.18(iv), Ch.9, Notations H, Notations H, Notations K.
Encodings:: BibTeX

… ►

M. Jimbo, T. Miwa, Y. Môri, and M. Sato (1980) Density matrix of an impenetrable Bose gas and the fifth Painlevé transcendent. Phys. D 1 (1), pp. 80–158.

ⓘ

External Links:: ISSN 0167-2789, Document, MathReview, ZentralBlatt
Referenced by:: §32.16.
Encodings:: BibTeX

… ►

JTEM (website) Java Tools for Experimental Mathematics

ⓘ

Notes:: Single and double precision. Contains packages to compute elliptic functions, Riemann theta functions and their derivatives, and Riemann matrices for Riemann surfaces.
External Links:: Home Page
Referenced by:: § ‣ Software Cross Index.
Encodings:: BibTeX

…

… ►

REDUCE (free interactive system)

ⓘ

Notes:: Symbolic and extended-precision general purpose computer algebra system.
External Links:: Home Page
Referenced by:: § ‣ Software Cross Index.
Encodings:: BibTeX

… ►

G. F. Remenets (1973) Computation of Hankel (Bessel) functions of complex index and argument by numerical integration of a Schläfli contour integral. Ž. Vyčisl. Mat. i Mat. Fiz. 13, pp. 1415–1424, 1636.

ⓘ

Notes:: English translation in U.S.S.R. Computational Math. and Math. Phys. 13(6), pp. 58–67
External Links:: ISSN 0044-4669, Document, MathReview (H. Zegeling), ZentralBlatt
Referenced by:: §10.74(iii).
Encodings:: BibTeX

… ►

D. St. P. Richards (2004) Total positivity properties of generalized hypergeometric functions of matrix argument. J. Statist. Phys. 116 (1-4), pp. 907–922.

ⓘ

External Links:: ISSN 0022-4715, Document, MathReview (Stamatis Koumandos), ZentralBlatt
Referenced by:: §35.9.
Encodings:: BibTeX

… ►

M. Robnik (1980) An extremum property of the

n

-dimensional sphere. J. Phys. A 13 (10), pp. L349–L351.

ⓘ

External Links:: ISSN 0305-4470, Document, MathReview
Referenced by:: §5.19(iii).
Encodings:: BibTeX

… ►

M. Rotenberg, R. Bivins, N. Metropolis, and J. K. Wooten, Jr. (1959) The

3

-

j

and

6

-

j

Symbols. The Technology Press, MIT, Cambridge, MA.

ⓘ

External Links:: ISBN 0-262-18004-9
Referenced by:: (34.1.1), §34.1, §34.1, §34.14, Erratum (V1.0.14) for Section 34.1, Erratum (V1.0.15) for Section 34.1.
Encodings:: BibTeX

…

matrix, index notation for m by n

10 matching pages

1: 1.2 Elementary Algebra

2: Bibliography M

Bibliography M

3: 18.39 Applications in the Physical Sciences

§18.39(iv) Coulomb–Pollaczek Polynomials and J-Matrix Methods

4: Bibliography S

5: Bibliography C

6: Bibliography I

7: Bibliography G

8: Bibliography W

9: Bibliography J

10: Bibliography R