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11: Philip J. Davis

… ►In 1957, Davis took over as Chief, Numerical Analysis Section when John Todd and his wife Olga Taussky-Todd, feeling a strong pull toward teaching and research, left to pursue full-time positions at the California Institute of Technology. … ►NBS mathematician Irene Stegun took over management of the A&S project which was already well on its way, and led the work to publication in 1964. … ►Davis’s comments about our uninspired graphs sparked the research and design of techniques for creating interactive 3D visualizations of function surfaces, which grew in sophistication as our knowledge and the technology for developing 3D graphics on the web advanced over the years. Today the DLMF contains close to 600 2D and 3D graphs and more than 200 interactive 3D visualizations. …

12: Bibliography N

… ►

M. Nardin, W. F. Perger, and A. Bhalla (1992b) Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes. J. Comput. Appl. Math. 39 (2), pp. 193–200.

ⓘ

Notes:: Extended-precision Fortran evaluator, minimum accuracy 9S, maximum accuracy 13S.
External Links:: ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt
Referenced by:: §13.32(iii).
Encodings:: BibTeX

… ►

H. M. Nussenzveig (1992) Diffraction Effects in Semiclassical Scattering. Montroll Memorial Lecture Series in Mathematical Physics, Cambridge University Press.

ⓘ

Notes:: Also available electronically through Cambridge Books Online, ISBN 9780511599903.
External Links:: ISBN 9780521383189, Document
Referenced by:: §9.16, §9.16.
Encodings:: BibTeX

…

13: Bibliography U

… ►

Unpublished Mathematical Tables (1944) Mathematics of Computation Unpublished Mathematical Tables Collection.

ⓘ

Notes:: Archives of American Mathematics, Center for American History, The University of Texas at Austin. Covers 1944–1994. An online guide is arranged chronologically by date of issuance within Mathematics of Computation
External Links:: Guide
Referenced by:: §27.21.
Encodings:: BibTeX

…

14: Frank W. J. Olver

… ►Most notably, he served as the Editor-in-Chief and Mathematics Editor of the online NIST Digital Library of Mathematical Functions and its 966-page print companion, the NIST Handbook of Mathematical Functions (Cambridge University Press, 2010). …

15: About the Project

… ►They were selected as recognized leaders in the research communities interested in the mathematics and applications of special functions and orthogonal polynomials; in the presentation of mathematics reference information online and in handbooks; and in the presentation of mathematics on the web. …

16: Bibliography O

… ►

T. Oliveira e Silva (2006) Computing

\pi(x)

: The combinatorial method. Revista do DETUA 4 (6), pp. 759–768.

ⓘ

Notes:: Online fulltext contains postpublication annotations.
External Links:: FullText
Referenced by:: §27.18.
Encodings:: BibTeX

… ►

F. W. J. Olver (1964b) Error bounds for asymptotic expansions in turning-point problems. J. Soc. Indust. Appl. Math. 12 (1), pp. 200–214.

ⓘ

External Links:: Document, MathReview (N. D. Kazarinoff), ZentralBlatt
Referenced by:: §2.8(iii).
Encodings:: BibTeX

…

17: Bibliography L

… ►

D. W. Lozier and F. W. J. Olver (1994) Numerical Evaluation of Special Functions. In Mathematics of Computation 1943–1993: A Half-Century of Computational Mathematics (Vancouver, BC, 1993), Proc. Sympos. Appl. Math., Vol. 48, pp. 79–125.

ⓘ

Notes:: An updated version exists online.
External Links:: FullText, MathReview (John P. Coleman), ZentralBlatt
Referenced by:: Ch.3.
Encodings:: BibTeX

… ►

Y. L. Luke and J. Wimp (1963) Jacobi polynomial expansions of a generalized hypergeometric function over a semi-infinite ray. Math. Comp. 17 (84), pp. 395–404.

ⓘ

External Links:: FullText, MathReview (I. A. Stegun), ZentralBlatt
Referenced by:: 2nd item.
Encodings:: BibTeX

…

18: 1.18 Linear Second Order Differential Operators and Eigenfunction Expansions

… ►A complex linear vector space

V

is called an inner product space if an inner product

\left\langle u,v\right\rangle\in\mathbb{C}

is defined for all

u,v\in V

with the properties: (i)

\left\langle u,v\right\rangle

is complex linear in

u

; (ii)

\left\langle u,v\right\rangle=\overline{\left\langle v,u\right\rangle}

; (iii)

\left\langle v,v\right\rangle\geq 0

; (iv) if

\left\langle v,v\right\rangle=0

then

v=0

. …Two elements

u

and

v

V

are orthogonal if

\left\langle u,v\right\rangle=0

. … ►Functions

f,g\in L^{2}\left(X,\,\mathrm{d}\alpha\right)

for which

\left\langle f-g,f-g\right\rangle=0

are identified with each other. … ►,

\left\langle u_{\lambda},u_{\lambda^{\prime}}\right\rangle=0

, for

\lambda\neq\lambda^{\prime}

. … ►The adjoint

{T}^{*}

T

does satisfy

\left\langle Tf,g\right\rangle=\left\langle f,{T}^{*}g\right\rangle

where

\left\langle f,g\right\rangle=\int_{a}^{b}f(x)g(x)\,\mathrm{d}x

. …

19: Bibliography W

… ►

J. V. Wehausen and E. V. Laitone (1960) Surface Waves. In Handbuch der Physik, Vol. 9, Part 3, pp. 446–778.

ⓘ

External Links:: Online edition, MathReview (F. Ursell), ZentralBlatt
Referenced by:: §11.12.
Encodings:: BibTeX

… ►

M. I. Weinstein and J. B. Keller (1985) Hill’s equation with a large potential. SIAM J. Appl. Math. 45 (2), pp. 200–214.

ⓘ

External Links:: ISSN 0036-1399, Document, MathReview (H. Hochstadt), ZentralBlatt
Referenced by:: §29.7(ii).
Encodings:: BibTeX

…

20: 1.2 Elementary Algebra

… ►

1.2.40

\left\langle\mathbf{u},\mathbf{v}\right\rangle=\sum_{i=1}^{n}u_{i}\overline{v_% {i}}={\mathbf{v}}^{{\rm H}}\mathbf{u}.

ⓘ

Defines:: $\left\langle\NVar{\mathbf{u}},\NVar{\mathbf{v}}\right\rangle$ : inner product over vectors
Symbols:: ${\NVar{\mathbf{A}}}^{{\rm H}}$ : Hermitian conjugate of matrix, $\overline{\NVar{z}}$ : complex conjugate, $n$ : nonnegative integer, $\mathbf{v}$ : column vector and $\mathbf{u}$ : column vector
Referenced by:: §1.18(i), §1.2(v)
Permalink:: http://dlmf.nist.gov/1.2.E40
Encodings:: pMML, png, TeX
See also:: Annotations for §1.2(v), §1.2(v), §1.2 and Ch.1

… ►

1.2.41

\left\langle\mathbf{u},\mathbf{v}\right\rangle=\overline{\left\langle\mathbf{v% },\mathbf{u}\right\rangle},

ⓘ

Symbols:: $\overline{\NVar{z}}$ : complex conjugate, $\left\langle\NVar{\mathbf{u}},\NVar{\mathbf{v}}\right\rangle$ : inner product over vectors, $\mathbf{v}$ : column vector and $\mathbf{u}$ : column vector
Permalink:: http://dlmf.nist.gov/1.2.E41
Encodings:: pMML, png, TeX
See also:: Annotations for §1.2(v), §1.2(v), §1.2 and Ch.1

… ►

1.2.42

\left\langle\alpha\mathbf{u},\beta\mathbf{v}\right\rangle=\alpha\overline{% \beta}\left\langle\mathbf{u},\mathbf{v}\right\rangle,

ⓘ

Symbols:: $\overline{\NVar{z}}$ : complex conjugate, $\left\langle\NVar{\mathbf{u}},\NVar{\mathbf{v}}\right\rangle$ : inner product over vectors, $\mathbf{v}$ : column vector and $\mathbf{u}$ : column vector
Referenced by:: §1.2(v)
Permalink:: http://dlmf.nist.gov/1.2.E42
Encodings:: pMML, png, TeX
See also:: Annotations for §1.2(v), §1.2(v), §1.2 and Ch.1

… ►

1.2.43

\left\langle\mathbf{v},\mathbf{v}\right\rangle=0,

ⓘ

Symbols:: $\left\langle\NVar{\mathbf{u}},\NVar{\mathbf{v}}\right\rangle$ : inner product over vectors and $\mathbf{v}$ : column vector
Permalink:: http://dlmf.nist.gov/1.2.E43
Encodings:: pMML, png, TeX
See also:: Annotations for §1.2(v), §1.2(v), §1.2 and Ch.1

… ►

1.2.44

\left\langle\mathbf{u},\mathbf{v}\right\rangle=0.

ⓘ

Symbols:: $\left\langle\NVar{\mathbf{u}},\NVar{\mathbf{v}}\right\rangle$ : inner product over vectors, $\mathbf{v}$ : column vector and $\mathbf{u}$ : column vector
Permalink:: http://dlmf.nist.gov/1.2.E44
Encodings:: pMML, png, TeX
See also:: Annotations for §1.2(v), §1.2(v), §1.2 and Ch.1

…