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$n$	$p_{n}$	$p_{n+10}$	$p_{n+20}$	$p_{n+30}$	$p_{n+40}$	$p_{n+50}$	$p_{n+60}$	$p_{n+70}$	$p_{n+80}$	$p_{n+90}$
…

Ince (1940a) tabulates the eigenvalues $a^{m}_{\nu}\left(k^{2}\right)$ , $b^{m+1}_{\nu}\left(k^{2}\right)$ (with $a^{2m+1}_{\nu}$ and $b^{2m+1}_{\nu}$ interchanged) for $k^{2}=0.1,0.5,0.9$ , $\nu=-\frac{1}{2},0(1)25$ , and $m=0,1,2,3$ . Precision is 4D.

►

•

Arscott and Khabaza (1962) tabulates the coefficients of the polynomials $P$ in Table 29.12.1 (normalized so that the numerically largest coefficient is unity, i.e. monic polynomials), and the corresponding eigenvalues $h$ for $k^{2}=0.1(.1)0.9$ , $n=1(1)30$ . Equations from §29.6 can be used to transform to the normalization adopted in this chapter. Precision is 6S.

13: Bibliography

… ►

A. R. Ahmadi and S. E. Widnall (1985) Unsteady lifting-line theory as a singular-perturbation problem. J. Fluid Mech 153, pp. 59–81.

ⓘ

External Links:: Document, ZentralBlatt
Referenced by:: §11.12.
Encodings:: BibTeX

… ►

W. A. Al-Salam and L. Carlitz (1965) Some orthogonal

q

-polynomials. Math. Nachr. 30, pp. 47–61.

ⓘ

External Links:: ISSN 0025-584X, Document, MathReview (A. E. Danese), ZentralBlatt
Referenced by:: §18.27(vii).
Encodings:: BibTeX

… ►

G. E. Andrews (2001) Bailey’s Transform, Lemma, Chains and Tree. In Special Functions 2000: Current Perspective and Future Directions (Tempe, AZ), J. Bustoz, M. E. H. Ismail, and S. K. Suslov (Eds.), NATO Sci. Ser. II Math. Phys. Chem., Vol. 30, pp. 1–22.

ⓘ

External Links:: ISBN 0-7923-7119-4, MathReview, ZentralBlatt
Referenced by:: §17.12.
Encodings:: BibTeX

… ►

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

L

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

ⓘ

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 (1975) Critical points of smooth functions, and their normal forms. Uspehi Mat. Nauk 30 (5(185)), pp. 3–65 (Russian).

ⓘ

Notes:: In Russian. English translation: Russian Math. Surveys, 30(1975), no. 5, pp. 1–75.
External Links:: Document, MathReview (D. Siersma), ZentralBlatt
Referenced by:: §36.2(i), Ch.36.
Encodings:: BibTeX

…

14: 26.9 Integer Partitions: Restricted Number and Part Size

… ►See Table 26.9.1. … ►

Table 26.9.1: Partitions

p_{k}\left(n\right)

► ►►►►

$n$	$k$
$n$	…
9	0	1	5	12	18	23	26	28	29	30	30
10	0	1	6	14	23	30	35	38	40	41	42

► …

15: 26.4 Lattice Paths: Multinomial Coefficients and Set Partitions

… ►Table 26.4.1 gives numerical values of multinomials and partitions

\lambda,M_{1},M_{2},M_{3}

for

1\leq m\leq n\leq 5

. … ►

Table 26.4.1: Multinomials and partitions.

► ►►►►

$n$	$m$	$\lambda$	$M_{1}$	$M_{2}$	$M_{3}$
…
$5$	$2$	$1^{1},4^{1}$	$5$	$30$	$5$
…
$5$	$3$	$1^{1},2^{2}$	$30$	$15$	$15$
…

► …

16: Bibliography F

… ►

B. R. Fabijonas, D. W. Lozier, and F. W. J. Olver (2004) Computation of complex Airy functions and their zeros using asymptotics and the differential equation. ACM Trans. Math. Software 30 (4), pp. 471–490.

ⓘ

External Links:: ISSN 0098-3500, Document, MathReview, ZentralBlatt
Referenced by:: §9.17(ii), §9.17(v), §9.8(iv).
Encodings:: BibTeX

… ►

B. R. Fabijonas (2004) Algorithm 838: Airy functions. ACM Trans. Math. Software 30 (4), pp. 491–501.

ⓘ

Notes:: Single- and double-precision Fortran, maximum accuracy 32S.
External Links:: ISSN 0098-3500, Document, Code, MathReview Entry, ZentralBlatt
Referenced by:: 3rd item, 2nd item, 1st item.
Encodings:: BibTeX

… ►

C. Ferreira, J. L. López, and E. Pérez Sinusía (2013a) The third Appell function for one large variable. J. Approx. Theory 165, pp. 60–69.

ⓘ

External Links:: ISSN 0021-9045, Document, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §16.13, §16.13.
Encodings:: BibTeX

… ►

H. E. Fettis (1976) Complex roots of

\sin z=az

\cos z=az

, and

\cosh z=az

. Math. Comp. 30 (135), pp. 541–545.

ⓘ

External Links:: FullText, MathReview (Gerhard Merz), ZentralBlatt
Referenced by:: §4.46.
Encodings:: BibTeX

… ►

A. S. Fokas and Y. C. Yortsos (1981) The transformation properties of the sixth Painlevé equation and one-parameter families of solutions. Lett. Nuovo Cimento (2) 30 (17), pp. 539–544.

ⓘ

External Links:: ISSN 0024-1318, MathReview (D. A. Lutz)
Referenced by:: §32.10(vi).
Encodings:: BibTeX

…

17: 3.4 Differentiation

… ►

B_{-2}^{6}=\tfrac{1}{60}(9-9t-30t^{2}+20t^{3}+5t^{4}-3t^{5}),

… ►

B_{2}^{6}=-\tfrac{1}{60}(9+9t-30t^{2}-20t^{3}+5t^{4}+3t^{5}),

… ►For corresponding formulas for second, third, and fourth derivatives, with

t=0

, see Collatz (1960, Table III, pp. 538–539). … ►The results in this subsection for the partial derivatives follow from Panow (1955, Table 10). … ►For additional formulas involving values of

\nabla^{2}u

and

\nabla^{4}u

on square, triangular, and cubic grids, see Collatz (1960, Table VI, pp. 542–546). …

18: 24.20 Tables

§24.20 Tables

… ►Wagstaff (1978) gives complete prime factorizations of

N_{n}

and

E_{n}

for

n=20(2)60

and

n=8(2)42

, respectively. In Wagstaff (2002) these results are extended to

n=60(2)152

and

n=40(2)88

, respectively, with further complete and partial factorizations listed up to

n=300

and

n=200

, respectively. ►For information on tables published before 1961 see Fletcher et al. (1962, v. 1, §4) and Lebedev and Fedorova (1960, Chapters 11 and 14).

19: Bibliography T

… ►

J. D. Talman (1983) LSFBTR: A subroutine for calculating spherical Bessel transforms. Comput. Phys. Comm. 30 (1), pp. 93–99.

ⓘ

Notes:: Single-precision Fortran.
External Links:: ISSN 0010-4655, Document, Code
Referenced by:: 9th item.
Encodings:: BibTeX

… ►

N. M. Temme (1979a) An algorithm with ALGOL 60 program for the computation of the zeros of ordinary Bessel functions and those of their derivatives. J. Comput. Phys. 32 (2), pp. 270–279.

ⓘ

External Links:: Document, ZentralBlatt
Referenced by:: §10.74(vi), §10.77(x).
Encodings:: BibTeX

… ►

N. M. Temme (1983) The numerical computation of the confluent hypergeometric function

{U}(a,\,b,\,z)

. Numer. Math. 41 (1), pp. 63–82.

ⓘ

Notes:: Algol 60 variable-precision procedures are included.
External Links:: ISSN 0029-599X, Document, MathReview (H. E. Fettis), ZentralBlatt
Referenced by:: §13.29(iv), §13.32(ii).
Encodings:: BibTeX

… ►

R. F. Tooper and J. Mark (1968) Simplified calculation of

\mathrm{Ei}(x)

for positive arguments, and a short table of

\mathrm{Shi}(x)

. Math. Comp. 22 (102), pp. 448–449.

ⓘ

External Links:: FullText, Document, ZentralBlatt
Referenced by:: §6.18(i).
Encodings:: BibTeX

… ►

H. Triebel (1965) Über die Lamésche Differentialgleichung. Math. Nachr. 30, pp. 137–154 (German).

ⓘ

External Links:: Document, MathReview (M. J. O. Strutt), ZentralBlatt
Referenced by:: §29.18(iv).
Encodings:: BibTeX

…

20: 13.30 Tables

§13.30 Tables

… ►

•

Zhang and Jin (1996, pp. 411–423) tabulates $M\left(a,b,x\right)$ and $U\left(a,b,x\right)$ for $a=-5(.5)5$ , $b=0.5(.5)5$ , and $x=0.1,1,5,10,20,30$ , 8S (for $M\left(a,b,x\right)$ ) and 7S (for $U\left(a,b,x\right)$ ).

►For other tables prior to 1961 see Fletcher et al. (1962) and Lebedev and Fedorova (1960).