DLMF: Untitled Document

… ►

p\left(\mathcal{D}^{\prime}3,n\right)

denotes the number of partitions of

n

into parts with difference at least 3, except that multiples of 3 must differ by at least 6. … ►

Table 26.10.1: Partitions restricted by difference conditions, or equivalently with parts from

A_{j,k}

.

► ►►►

	$p\left(\mathcal{D},n\right)$	$p\left(\mathcal{D}2,n\right)$	$p\left(\mathcal{D}2,\hbox{}\!\!\in\!T,n\right)$	$p\left(\mathcal{D}^{\prime}3,n\right)$
…
$20$	$64$	$31$	$20$	$18$

► …

… ►

H. S. Wall (1948) Analytic Theory of Continued Fractions. D. Van Nostrand Company, Inc., New York.

ⓘ

Notes:: Reprinted by Chelsea Publishing, New York, 1973 and AMS Chelsea Publishing, Providence, RI, 2000.
External Links:: ISBN 0-8218-2106-7, MathReview (R. C. Buck), ZentralBlatt
Referenced by:: §3.10(iii), §4.25, §4.9(i), §4.9(ii), Ch.4, §5.10.
Encodings:: BibTeX

… ►

R. S. Ward (1987) The Nahm equations, finite-gap potentials and Lamé functions. J. Phys. A 20 (10), pp. 2679–2683.

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External Links:: ISSN 0305-4470, Document, MathReview (James M. D’Archangelo), ZentralBlatt
Referenced by:: §29.19(ii).
Encodings:: BibTeX

…

… ►In the case

z=0

identities for theta functions become identities in the complex variable

q

, with

\left|q\right|<1

, that involve rational functions, power series, and continued fractions; see Adiga et al. (1985), McKean and Moll (1999, pp. 156–158), and Andrews et al. (1988, §10.7). …

… ►

G. Backenstoss (1970) Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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External Links:: Document
Referenced by:: §33.22(iv).
Encodings:: BibTeX

… ►

G. Blanch (1964) Numerical evaluation of continued fractions. SIAM Rev. 6 (4), pp. 383–421.

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External Links:: Document, MathReview (E. Frank), ZentralBlatt
Referenced by:: §3.10(iii), §3.10(ii).
Encodings:: BibTeX

… ►

R. P. Brent (1978a) A Fortran multiple-precision arithmetic package. ACM Trans. Math. Software 4 (1), pp. 57–70.

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External Links:: ISSN 0098-3500, Document
Referenced by:: 1st item.
Encodings:: BibTeX

►

R. P. Brent (1976) Fast multiple-precision evaluation of elementary functions. J. Assoc. Comput. Mach. 23 (2), pp. 242–251.

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External Links:: Document, MathReview (Amnon Barak), ZentralBlatt
Referenced by:: §4.45(i).
Encodings:: BibTeX

►

R. P. Brent (1978b) Algorithm 524: MP, A Fortran multiple-precision arithmetic package [A1]. ACM Trans. Math. Software 4 (1), pp. 71–81.

ⓘ

External Links:: ISSN 0098-3500, Document, Remark. GAMS (module 524; package TOMS)
Referenced by:: 3rd item, 1st item, 1st item, 1st item, 3rd item, 1st item, 1st item.
Encodings:: BibTeX

…

… ►

P. W. Lawrence, R. M. Corless, and D. J. Jeffrey (2012) Algorithm 917: complex double-precision evaluation of the Wright

\omega

function. ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.

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External Links:: ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §4.13, 2nd item, §4.48(iv).
Encodings:: BibTeX

… ►

D. J. Leeming (1977) An asymptotic estimate for the Bernoulli and Euler numbers. Canad. Math. Bull. 20 (1), pp. 109–111.

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External Links:: MathReview (D. H. Lehmer), ZentralBlatt
Referenced by:: §24.11.
Encodings:: BibTeX

… ►

W. J. Lentz (1976) Generating Bessel functions in Mie scattering calculations using continued fractions. Applied Optics 15 (3), pp. 668–671.

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Referenced by:: §3.10(iii), §3.10(iii), Erratum (V1.0.24) for Paragraph Steed’s Algorithm (in §3.10(iii)).
Encodings:: BibTeX

… ►

L. Lorentzen and H. Waadeland (1992) Continued Fractions with Applications. Studies in Computational Mathematics, North-Holland Publishing Co., Amsterdam.

ⓘ

External Links:: ISBN 0-444-89265-6, MathReview (Olav Njåstad), ZentralBlatt
Referenced by:: §1.12(ii), §1.12(iv), §1.12(v), §15.7, §18.13, §3.10(ii), §3.10(iii), §3.11(iv), §4.25, §4.39, §4.9(i), §4.9(ii), §5.10, §6.9, §7.18(v), §7.9.
Encodings:: BibTeX

… ►

E. R. Love (1972b) Two index laws for fractional integrals and derivatives. J. Austral. Math. Soc. 14, pp. 385–410.

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External Links:: Document, MathReview (C. Fox), ZentralBlatt
Referenced by:: §1.15(vi), §1.15(vii).
Encodings:: BibTeX

…

… ►

H. Davenport (2000) Multiplicative Number Theory. 3rd edition, Graduate Texts in Mathematics, Vol. 74, Springer-Verlag, New York.

ⓘ

Notes:: Revised and with a preface by Hugh L. Montgomery
External Links:: ISBN 0-387-95097-4, MathReview, ZentralBlatt
Referenced by:: §27.12.
Encodings:: BibTeX

… ►

J. Deltour (1968) The computation of lattice frequency distribution functions by means of continued fractions. Physica 39 (3), pp. 413–423.

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External Links:: ISSN 0031-8914, Document, Link
Referenced by:: §18.40(ii).
Encodings:: BibTeX

… ►

K. Dilcher (2008) On multiple zeros of Bernoulli polynomials. Acta Arith. 134 (2), pp. 149–155.

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External Links:: ISSN 0065-1036, Document, MathReview (Arnold M. Adelberg), ZentralBlatt
Referenced by:: §24.12(iv).
Encodings:: BibTeX

… ►

B. Döring (1966) Complex zeros of cylinder functions. Math. Comp. 20 (94), pp. 215–222.

ⓘ

Notes:: For a numerical error in one of the zeros see Amos (1985).
External Links:: ISSN 0025-5718, FullText, MathReview, ZentralBlatt
Referenced by:: 2nd item.
Encodings:: BibTeX

… ►

T. M. Dunster (1989) Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions. SIAM J. Math. Anal. 20 (3), pp. 744–760.

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Notes:: (This reference has several typographical errors.)
External Links:: ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt
Referenced by:: §13.21(ii), §13.21(iii), §13.21(iv).
Encodings:: BibTeX

…

… ►

I. Gargantini and P. Henrici (1967) A continued fraction algorithm for the computation of higher transcendental functions in the complex plane. Math. Comp. 21 (97), pp. 18–29.

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External Links:: FullText, MathReview (D. C. Gilles), ZentralBlatt
Referenced by:: §10.74(v), §3.10(ii).
Encodings:: BibTeX

… ►

G. Gasper (1975) Formulas of the Dirichlet-Mehler Type. In Fractional Calculus and its Applications, B. Ross (Ed.), Lecture Notes in Math., Vol. 457, pp. 207–215.

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External Links:: MathReview (Mourad E. H. Ismail), ZentralBlatt
Referenced by:: §18.10(i).
Encodings:: BibTeX

… ►

W. Gautschi (1994) Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules. ACM Trans. Math. Software 20 (1), pp. 21–62.

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Notes:: For remark see same journal 24(1998), p. 355.
External Links:: Document, ISSN 0098-3500, GAMS (module 726; package TOMS), ZentralBlatt
Referenced by:: 2nd item, §3.5(v), §3.5(v).
Encodings:: BibTeX

… ►

A. Gil, J. Segura, and N. M. Temme (2014) Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:: Includes Fortran program claiming 12S accuracy
External Links:: ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt
Referenced by:: 3rd item, §10.77(ix).
Encodings:: BibTeX

… ►

Ya. I. Granovskiĭ, I. M. Lutzenko, and A. S. Zhedanov (1992) Mutual integrability, quadratic algebras, and dynamical symmetry. Ann. Phys. 217 (1), pp. 1–20.

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External Links:: ISSN 0003-4916, Link, MathReview (A. O. Barut), ZentralBlatt
Referenced by:: §18.38(iii).
Encodings:: BibTeX

…

§3.8 Nonlinear Equations

… ►has

n

zeros in

\mathbb{C}

, counting each zero according to its multiplicity. … ►The method converges locally and quadratically, except when the wanted quadratic factor is a multiple factor of

q(z)

. … ►Consider

x=20

and

j=19

. We have

p^{\mspace{1.0mu}\prime}(20)=19!

and

a_{19}=1+2+\dots+20=210

. …

fractional%20or%20multiple

11—18 of 18 matching pages

11: 26.10 Integer Partitions: Other Restrictions

12: Bibliography W

13: 20.11 Generalizations and Analogs

14: Bibliography B

15: Bibliography L

16: Bibliography D

17: Bibliography G

18: 3.8 Nonlinear Equations

§3.8 Nonlinear Equations