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21: Bibliography I

… ►

Y. Ikebe (1975) The zeros of regular Coulomb wave functions and of their derivatives. Math. Comp. 29, pp. 878–887.

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External Links:: ISSN 0025-5718, Document, MathReview, ZentralBlatt
Referenced by:: §3.8(iii).
Encodings:: BibTeX

… ►

A. E. Ingham (1933) An integral which occurs in statistics. Proceedings of the Cambridge Philosophical Society 29, pp. 271–276.

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External Links:: Document, ZentralBlatt
Referenced by:: §35.3(i), §35.3(ii).
Encodings:: BibTeX

… ►

A. Iserles, P. E. Koch, S. P. Nørsett, and J. M. Sanz-Serna (1991) On polynomials orthogonal with respect to certain Sobolev inner products. J. Approx. Theory 65 (2), pp. 151–175.

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External Links:: ISSN 0021-9045, Document, MathReview (R. A. Askey), ZentralBlatt
Referenced by:: §18.36(ii).
Encodings:: BibTeX

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M. E. H. Ismail and M. E. Muldoon (1995) Bounds for the small real and purely imaginary zeros of Bessel and related functions. Methods Appl. Anal. 2 (1), pp. 1–21.

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External Links:: ISSN 1073-2772, FullText, MathReview (Andrea Laforgia), ZentralBlatt
Referenced by:: §10.21(v).
Encodings:: BibTeX

… ►

M. E. H. Ismail (2000a) An electrostatics model for zeros of general orthogonal polynomials. Pacific J. Math. 193 (2), pp. 355–369.

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External Links:: ISSN 0030-8730, FullText, MathReview (T. Erber), ZentralBlatt
Referenced by:: §18.39(v).
Encodings:: BibTeX

…

22: 14.15 Uniform Asymptotic Approximations

… ►See also Temme (2015, Chapter 29). … ►See also Temme (2015, Chapter 29). … ►The points

x=\left(1-\alpha^{2}\right)^{1/2}

x=1

, and

x=\infty

are mapped to

y=\alpha^{2}

y=0

, and

y=-\infty

, respectively. … ►

§14.15(v) Large $\nu$ , $(\nu+\frac{1}{2})\delta\leq\mu\leq(\nu+\frac{1}{2})/\delta$

… ►uniformly with respect to

x\in[0,1)

and

\mu\in[\delta(\nu+\frac{1}{2}),\nu+\frac{1}{2}]

. …

23: 27.2 Functions

… ►where

p_{1},p_{2},\dots,p_{\nu\left(n\right)}

are the distinct prime factors of

n

, each exponent

a_{r}

is positive, and

\nu\left(n\right)

is the number of distinct primes dividing

n

. … ►The

\phi\left(n\right)

numbers

a,a^{2},\dots,a^{\phi\left(n\right)}

are relatively prime to

n

and distinct (mod

n

). …It is the special case

k=2

of the function

d_{k}\left(n\right)

that counts the number of ways of expressing

n

as the product of

k

factors, with the order of factors taken into account. … ►

27.2.12

\mu\left(n\right)=\begin{cases}1,&n=1,\\ (-1)^{\nu\left(n\right)},&a_{1}=a_{2}=\dots=a_{\nu\left(n\right)}=1,\\ 0,&\mbox{otherwise}.\end{cases}

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Defines:: $\mu\left(\NVar{n}\right)$ : Möbius function
Symbols:: $\nu\left(\NVar{n}\right)$ : number of distinct primes dividing a number, $n$ : positive integer and $a$ : primitive root
A&S Ref:: 24.3.1 I.A
Permalink:: http://dlmf.nist.gov/27.2.E12
Encodings:: pMML, png, TeX
See also:: Annotations for §27.2(i), §27.2 and Ch.27

… ►

Table 27.2.2: Functions related to division.

► ►►►

$n$	$\phi\left(n\right)$	$d\left(n\right)$	$\sigma\left(n\right)$	$n$	$\phi\left(n\right)$	$d\left(n\right)$	$\sigma\left(n\right)$	$n$	$\phi\left(n\right)$	$d\left(n\right)$	$\sigma\left(n\right)$	$n$	$\phi\left(n\right)$	$d\left(n\right)$	$\sigma\left(n\right)$
…
3	2	2	4	16	8	5	31	29	28	2	30	42	12	8	96
…

►

24: Bibliography

… ►

L. V. Ahlfors (1966) Complex Analysis: An Introduction of the Theory of Analytic Functions of One Complex Variable. 2nd edition, McGraw-Hill Book Co., New York.

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Notes:: A third edition was published in 1978 by McGraw-Hill, New York.
External Links:: MathReview (P. Lelong), ZentralBlatt
Referenced by:: §1.9(iii), §23.18.
Encodings:: BibTeX

… ►

S. Ahmed and M. E. Muldoon (1980) On the zeros of confluent hypergeometric functions. III. Characterization by means of nonlinear equations. Lett. Nuovo Cimento (2) 29 (11), pp. 353–358.

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External Links:: ISSN 0024-1318, MathReview (James M. Horner)
Referenced by:: §13.9(i).
Encodings:: BibTeX

… ►

D. W. Albrecht, E. L. Mansfield, and A. E. Milne (1996) Algorithms for special integrals of ordinary differential equations. J. Phys. A 29 (5), pp. 973–991.

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External Links:: ISSN 0305-4470, Document, MathReview, ZentralBlatt
Referenced by:: §32.10(i).
Encodings:: BibTeX

… ►

T. M. Apostol (1985b) Note on the trivial zeros of Dirichlet

L

-functions. Proc. Amer. Math. Soc. 94 (1), pp. 29–30.

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External Links:: ISSN 0002-9939, FullText, MathReview (Jerzy Kaczorowski), ZentralBlatt
Referenced by:: (25.15.7), (25.15.8), §25.15(ii), §25.15.
Encodings:: BibTeX

… ►

V. I. Arnol’d (1974) Normal forms of functions in the neighborhood of degenerate critical points. Uspehi Mat. Nauk 29 (2(176)), pp. 11–49 (Russian).

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Notes:: Collection of articles dedicated to the memory of Ivan Georgievič Petrovskiĭ (1901–1973), I. In Russian. English translation: Russian Math. Surveys, 29(1974), no. 2, pp. 10–50.
External Links:: Document, MathReview (G. R. Belickii), ZentralBlatt
Referenced by:: §36.2(i).
Encodings:: BibTeX

…