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1: DLMF Project News

error generating summary

2: Foreword

… ►However, we have also seen the birth of a new age of computing technology, which has not only changed how we utilize special functions, but also how we communicate technical information. …

3: Frank W. J. Olver

… ►Having witnessed the birth of the computer age firsthand (as a colleague of Alan Turing at NPL, for example), Olver is also well known for his contributions to the development and analysis of numerical methods for computing special functions. … ►He continued his editing work until the time of his death on April 22, 2013 at age 88.

4: Publications

… ►

A Special Functions Handbook for the Digital Age, Notices of the American Mathematical Society 58, 7 (2011), pp. 905–911.

…

5: 28 Mathieu Functions and Hill’s Equation

Chapter 28 Mathieu Functions and Hill’s Equation

…

6: Simon Ruijsenaars

… ►

28 Mathieu Functions and Hill’s Equation

7: Gerhard Wolf

… ►

28 Mathieu Functions and Hill’s Equation

…

8: 27.2 Functions

… ►

Table 27.2.1: Primes.

► ►►►

$n$	$p_n$	$p_{n+10}$	$p_{n+20}$	$p_{n+30}$	$p_{n+40}$	$p_{n+50}$	$p_{n+60}$	$p_{n+70}$	$p_{n+80}$	$p_{n+90}$
…
4	7	43	89	139	193	251	311	373	433	491
…

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►

Table 27.2.2: Functions related to division.

► ►►►►►

$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$	$n$	$\varphi \left(n\right)$	$d\left(n\right)$	$\sigma \left(n\right)$
…
2	1	2	3	15	8	4	24	28	12	6	56	41	40	2	42
3	2	2	4	16	8	5	31	29	28	2	30	42	12	8	96
…
12	4	6	28	25	20	3	31	38	18	4	60	51	32	4	72
…

►

9: 31.18 Methods of Computation

… ►The computation of the accessory parameter for the Heun functions is carried out via the continued-fraction equations (31.4.2) and (31.11.13) in the same way as for the Mathieu, Lamé, and spheroidal wave functions in Chapters 28–30.

10: Bibliography B

… ►

Algorithms for computing Bessel functions of half-integer order with complex arguments. Zh. Vychisl. Mat. i Mat. Fiz. 28 (10), pp. 1449–1460, 1597.

ⓘ

Notes:

English translation in U.S.S.R. Comput. Math. and Math. Phys. 28(1988), no. 5, 109–117

External Links:

ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.77(iv).

Encodings:

BibTeX

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Algorithms for evaluating spherical Bessel functions in the complex domain. Zh. Vychisl. Mat. i Mat. Fiz. 28 (12), pp. 1779–1788, 1918.

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Notes:

English translation in U.S.S.R. Comput. Math. and Math. Phys. 28(1988), no. 6, 122–128

External Links:

ISSN 0044-4669, Document, MathReview (Walter Gautschi), ZentralBlatt

Referenced by:

§10.77(iv).

Encodings:

BibTeX

… ►

Products of generalized hypergeometric series. Proc. London Math. Soc. (2) 28 (2), pp. 242–254.

ⓘ

External Links:

Document, ZentralBlatt

Referenced by:

§16.12.

Encodings:

BibTeX

… ►

Some Geometric Aspects of Wave Motion: Wavefront Dislocations, Diffraction Catastrophes, Diffractals. In Geometry of the Laplace Operator (Proc. Sympos. Pure Math., Univ. Hawaii, Honolulu, Hawaii, 1979), Vol. 36, pp. 13–28.

ⓘ

External Links:

MathReview (I. Stewart), ZentralBlatt

Referenced by:

§36.14(i).

Encodings:

BibTeX

… ►

Two cold atoms in a harmonic trap. Found. Phys. 28 (4), pp. 549–559.

ⓘ

External Links:

Document

Referenced by:

§12.17.

Encodings:

BibTeX

…