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31—40 of 221 matching pages

31: Bibliography S

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R. Shail (1980) On integral representations for Lamé and other special functions. SIAM J. Math. Anal. 11 (4), pp. 702–723.

ⓘ

External Links:: ISSN 0036-1410, Document, MathReview (R. K. Gupta), ZentralBlatt
Referenced by:: §29.17(i), §29.8.
Encodings:: BibTeX

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N. T. Shawagfeh (1992) The Laplace transforms of products of Airy functions. Dirāsāt Ser. B Pure Appl. Sci. 19 (2), pp. 7–11.

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External Links:: ISSN 0253-424X, MathReview
Referenced by:: §9.10(v).
Encodings:: BibTeX

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A. Sidi (2010) A simple approach to asymptotic expansions for Fourier integrals of singular functions. Appl. Math. Comput. 216 (11), pp. 3378–3385.

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External Links:: ISSN 0096-3003, Document, Link, MathReview Entry, ZentralBlatt
Referenced by:: §2.3(iv).
Encodings:: BibTeX

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R. Sips (1965) Représentation asymptotique de la solution générale de l’équation de Mathieu-Hill. Acad. Roy. Belg. Bull. Cl. Sci. (5) 51 (11), pp. 1415–1446.

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External Links:: ZentralBlatt
Referenced by:: §28.8(ii).
Encodings:: BibTeX

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K. Soni (1980) Exact error terms in the asymptotic expansion of a class of integral transforms. I. Oscillatory kernels. SIAM J. Math. Anal. 11 (5), pp. 828–841.

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External Links:: ISSN 0036-1410, Document, MathReview (John S. Lew), ZentralBlatt
Referenced by:: §2.5(ii).
Encodings:: BibTeX

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32: Bibliography C

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L. Carlitz (1960) Note on Nörlund’s polynomial

B_{n}^{(z)}

. Proc. Amer. Math. Soc. 11 (3), pp. 452–455.

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External Links:: FullText, MathReview (M. P. Drazin), ZentralBlatt
Referenced by:: §26.1, §26.1, Notations S, Notations S.
Encodings:: BibTeX

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P. A. Clarkson (2003b) The fourth Painlevé equation and associated special polynomials. J. Math. Phys. 44 (11), pp. 5350–5374.

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External Links:: ISSN 0022-2488, Document, MathReview, ZentralBlatt
Referenced by:: §32.8(iv).
Encodings:: BibTeX

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J. A. Cochran (1963) Further formulas for calculating approximate values of the zeros of certain combinations of Bessel functions. IEEE Trans. Microwave Theory Tech. 11 (6), pp. 546–547.

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External Links:: ISSN 0018-9480, FullText
Referenced by:: §10.21(x).
Encodings:: BibTeX

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M. Colman, A. Cuyt, and J. Van Deun (2011) Validated computation of certain hypergeometric functions. ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.

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External Links:: ISSN 0098-3500, Document, FullText, MathReview Entry, ZentralBlatt
Referenced by:: §13.29(v), §15.19(v).
Encodings:: BibTeX

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F. Cooper, A. Khare, and A. Saxena (2006) Exact elliptic compactons in generalized Korteweg-de Vries equations. Complexity 11 (6), pp. 30–34.

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External Links:: ISSN 1076-2787, Document, MathReview
Referenced by:: §19.6(i).
Encodings:: BibTeX

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33: 26.6 Other Lattice Path Numbers

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Table 26.6.1: Delannoy numbers

D(m,n)

► ►►►►

$m$	$n$
$m$	…
1	1	3	5	7	9	11	13	15	17	19	21
…
5	1	11	61	231	681	1683	3653	7183	13073	22363	36365
…

► … ►

Table 26.6.2: Motzkin numbers

M(n)

► ►►►

$n$	$M(n)$	$n$	$M(n)$	$n$	$M(n)$	$n$	$M(n)$	$n$	$M(n)$
…
3	4	7	127	11	5798	15	3 10572	19	181 99284

► … ►

Table 26.6.4: Schröder numbers

r(n)

► ►►►►

$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$
…
$1$	$2$	$5$	$394$	$9$	$2\;06098$	$13$	$1420\;78746$	$17$	$11\;18180\;26018$
…
$3$	$22$	$7$	$8558$	$11$	$52\;93446$	$15$	$39376\;03038$	$19$	$323\;67243\;17174$

► …

34: Bibliography M

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M. Mazzocco (2001a) Rational solutions of the Painlevé VI equation. J. Phys. A 34 (11), pp. 2281–2294.

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External Links:: ISSN 0305-4470, Document, MathReview (Shun Shimomura), ZentralBlatt
Referenced by:: §32.8(vi).
Encodings:: BibTeX

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T. Morita (1978) Calculation of the complete elliptic integrals with complex modulus. Numer. Math. 29 (2), pp. 233–236.

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Notes:: An Algol procedure for calculating the complete elliptic integrals of the first and the second kind with complex modulus $k$ is included.
External Links:: ISSN 0029-599X, Document, MathReview (H. E. Fettis), ZentralBlatt
Referenced by:: §19.36(ii), §19.39(ii).
Encodings:: BibTeX

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L. Moser and M. Wyman (1958b) Stirling numbers of the second kind. Duke Math. J. 25 (1), pp. 29–43.

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External Links:: Document, MathReview (A. Sade), ZentralBlatt
Referenced by:: §26.1, §26.8(vii), Notations S.
Encodings:: BibTeX

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D. Müller, B. G. Kelly, and J. J. O’Brien (1994) Spheroidal eigenfunctions of the tidal equation. Phys. Rev. Lett. 73 (11), pp. 1557–1560.

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External Links:: ISSN 0031-9007, Document, MathReview, ZentralBlatt
Referenced by:: §30.13(v).
Encodings:: BibTeX

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L. A. Muraveĭ (1976) Zeros of the function

Ai^{\prime}(z)-\sigma Ai(z)

. Differential Equations 11, pp. 797–811.

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External Links:: ZentralBlatt
Referenced by:: §9.9(i).
Encodings:: BibTeX

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35: 8.26 Tables

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•

Pearson (1968) tabulates $I_{x}\left(a,b\right)$ for $x=0.01(.01)1$ , $a,b=0.5(.5)11(1)50$ , with $b\leq a$ , to 7D.

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•

Chiccoli et al. (1988) presents a short table of $E_{p}\left(x\right)$ for $p=-\tfrac{9}{2}(1)-\tfrac{1}{2}$ , $0\leq x\leq 200$ to 14S.

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37: 26.10 Integer Partitions: Other Restrictions

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

A_{j,k}

► ►►►►►►

	$p\left(\mathcal{D},n\right)$	$p\left(\mathcal{D}2,n\right)$	$p\left(\mathcal{D}2,\hbox{}\!\!\in\!T,n\right)$	$p\left(\mathcal{D}^{\prime}3,n\right)$
…
$9$	$8$	$5$	$3$	$3$
…
$11$	$12$	$7$	$4$	$5$
…
$15$	$27$	$14$	$9$	$9$
$16$	$32$	$17$	$11$	$10$
…

► … ►Note that

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

, with strict inequality for

n\geq 9

. …

38: 26.5 Lattice Paths: Catalan Numbers

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Table 26.5.1: Catalan numbers.

► ►►►►

$n$	$C\left(n\right)$	$n$	$C\left(n\right)$	$n$	$C\left(n\right)$
…
2	2	9	4862	16	353 57670
…
4	14	11	58786	18	4776 38700
…

► …

39: 26.16 Multiset Permutations

… ►Thus

\mathop{\mathrm{inv}}(351322453154)=4+8+0+3+1+1+2+3+1+0+1=24

, and

\mathop{\mathrm{maj}}(351322453154)=2+4+8+9+11=34.

…

Yakovleva (1969) tabulates Fock’s functions $U(x)\equiv\sqrt{\pi}\operatorname{Bi}\left(x\right)$ , $U^{\prime}(x)=\sqrt{\pi}\operatorname{Bi}'\left(x\right)$ , $V(x)\equiv\sqrt{\pi}\operatorname{Ai}\left(x\right)$ , $V^{\prime}(x)=\sqrt{\pi}\operatorname{Ai}'\left(x\right)$ for $x=-9(.001)9$ . Precision is 7S.

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•

National Bureau of Standards (1958) tabulates $A_{0}(x)\equiv\pi\operatorname{Hi}\left(-x\right)$ and $-A_{0}^{\prime}(x)\equiv\pi\operatorname{Hi}'\left(-x\right)$ for $x=0(.01)1(.02)5(.05)11$ and $1/x=0.01(.01)0.1$ ; $\int_{0}^{x}A_{0}(t)\,\mathrm{d}t$ for $x=0.5,1(1)11$ . Precision is 8D.

►

•

Nosova and Tumarkin (1965) tabulates $e_{0}(x)\equiv\pi\operatorname{Hi}\left(-x\right)$ , $e^{\prime}_{0}(x)=-\pi\operatorname{Hi}'\left(-x\right)$ , $\widetilde{e}_{0}(-x)\equiv-\pi\operatorname{Gi}\left(x\right)$ , $\widetilde{e}^{\mspace{2.0mu}\prime}_{0}(-x)=\pi\operatorname{Gi}'\left(x\right)$ for $x=-1(.01)10$ ; 7D. Also included are the real and imaginary parts of $e_{0}(z)$ and $ie^{\prime}_{0}(z)$ , where $z=iy$ and $y=0(.01)9$ ; 6-7D.

►

•

Gil et al. (2003c) tabulates the only positive zero of $\operatorname{Gi}'\left(z\right)$ , the first 10 negative real zeros of $\operatorname{Gi}\left(z\right)$ and $\operatorname{Gi}'\left(z\right)$ , and the first 10 complex zeros of $\operatorname{Gi}\left(z\right)$ , $\operatorname{Gi}'\left(z\right)$ , $\operatorname{Hi}\left(z\right)$ , and $\operatorname{Hi}'\left(z\right)$ . Precision is 11 or 12S.

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.世界杯体彩串买『网址:mxsty.cc』.陪看世界杯女孩.m6q3s2-2022年11月29日7时0分9秒.字符>wcamcs

31—40 of 221 matching pages

31: Bibliography S

32: Bibliography C

33: 26.6 Other Lattice Path Numbers

34: Bibliography M

35: 8.26 Tables

36: Richard B. Paris

37: 26.10 Integer Partitions: Other Restrictions

38: 26.5 Lattice Paths: Catalan Numbers

39: 26.16 Multiset Permutations

40: 9.18 Tables