Stirling%20numbers%20%28first%20and%20second%20kinds%29

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31—40 of 428 matching pages

31: Bibliography O

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A. B. Olde Daalhuis (2005b) Hyperasymptotics for nonlinear ODEs. II. The first Painlevé equation and a second-order Riccati equation. Proc. R. Soc. Lond. Ser. A Math. Phys. Eng. Sci. 461 (2062), pp. 3005–3021.

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External Links:: ISSN 1364-5021, Document, MathReview, ZentralBlatt
Referenced by:: §2.11(v), §32.12(i).
Encodings:: BibTeX

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J. Oliver (1977) An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series. J. Inst. Math. Appl. 20 (3), pp. 379–391.

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External Links:: Document, MathReview (David L. Elliott), ZentralBlatt
Referenced by:: §3.11(ii).
Encodings:: BibTeX

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F. W. J. Olver (1977b) Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities. SIAM J. Math. Anal. 8 (4), pp. 673–700.

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External Links:: Document, MathReview (W. Wasow), ZentralBlatt
Referenced by:: §2.8(v).
Encodings:: BibTeX

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H. Oser (1960) Algorithm 22: Riccati-Bessel functions of first and second kind. Comm. ACM 3 (11), pp. 600–601.

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Notes:: Includes Algol code, minimum accuracy 9S. For certification see same journal 13(1970), p. 448.
External Links:: ISSN 0001-0782, Document
Referenced by:: §10.77(ii).
Encodings:: BibTeX

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32: William P. Reinhardt

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20 Theta Functions

… ►In November 2015, Reinhardt was named Senior Associate Editor of the DLMF and Associate Editor for Chapters 20, 22, and 23.

33: 26.2 Basic Definitions

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Table 26.2.1: Partitions

p\left(n\right)

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$n$	$p\left(n\right)$	$n$	$p\left(n\right)$	$n$	$p\left(n\right)$
…
3	3	20	627	37	21637
…

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34: Bibliography N

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D. Naylor (1989) On an integral transform involving a class of Mathieu functions. SIAM J. Math. Anal. 20 (6), pp. 1500–1513.

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External Links:: ISSN 0036-1410, Document, MathReview (K. C. Gupta), ZentralBlatt
Referenced by:: §28.26(ii).
Encodings:: BibTeX

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W. J. Nellis and B. C. Carlson (1966) Reduction and evaluation of elliptic integrals. Math. Comp. 20 (94), pp. 223–231.

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External Links:: FullText, MathReview (I. A. Stegun), ZentralBlatt
Referenced by:: §19.37(iv).
Encodings:: BibTeX

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E. Neuman (2004) Inequalities involving Bessel functions of the first kind. JIPAM. J. Inequal. Pure Appl. Math. 5 (4), pp. Article 94, 4 pp. (electronic).

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External Links:: ISSN 1443-5756, FullText, MathReview, ZentralBlatt
Referenced by:: §10.14.
Encodings:: BibTeX

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E. W. Ng and M. Geller (1969) A table of integrals of the error functions. J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.

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Notes:: See for additions and corrections same journal, Sect. B 75, 149–163 (1975)
External Links:: MathReview, ZentralBlatt
Referenced by:: §7.14(iii), §7.21, §7.7(iii).
Encodings:: BibTeX

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35: 6.19 Tables

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Zhang and Jin (1996, pp. 652, 689) includes $\operatorname{Si}\left(x\right)$ , $\operatorname{Ci}\left(x\right)$ , $x=0(.5)20(2)30$ , 8D; $\operatorname{Ei}\left(x\right)$ , $E_{1}\left(x\right)$ , $x=[0,100]$ , 8S.

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Abramowitz and Stegun (1964, Chapter 5) includes the real and imaginary parts of $ze^{z}E_{1}\left(z\right)$ , $x=-19(1)20$ , $y=0(1)20$ , 6D; $e^{z}E_{1}\left(z\right)$ , $x=-4(.5)-2$ , $y=0(.2)1$ , 6D; $E_{1}\left(z\right)+\ln z$ , $x=-2(.5)2.5$ , $y=0(.2)1$ , 6D.

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Zhang and Jin (1996, pp. 690–692) includes the real and imaginary parts of $E_{1}\left(z\right)$ , $\pm x=0.5,1,3,5,10,15,20,50,100$ , $y=0(.5)1(1)5(5)30,50,100$ , 8S.

36: 10.3 Graphics

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See accompanying text — Figure 10.3.14: ${H^{(1)}_{5}}\left(x+iy\right)$ , $-20\leq x\leq 10$ , $-4\leq y\leq 4$ . … Magnify 3D Help

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37: 5.11 Asymptotic Expansions

… ►Wrench (1968) gives exact values of

g_{k}

up to

g_{20}

. …

38: 26.3 Lattice Paths: Binomial Coefficients

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Table 26.3.1: Binomial coefficients

\genfrac{(}{)}{0.0pt}{}{m}{n}

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$m$	$n$
$m$	…
6	1	6	15	20	15	6	1
…

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Table 26.3.2: Binomial coefficients

\genfrac{(}{)}{0.0pt}{}{m+n}{m}

for lattice paths.

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$m$	$n$
$m$	…
3	1	4	10	20	35	56	84	120	165
…

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39: Bibliography F

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FDLIBM (free C library)

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Notes:: The “Freely Distributable LIBM” package provides implementations of standard elementary functions plus a few higher functions, e.g. gamma. Double precision, maximum accuracy 20S. Developed by Sun Microsystems.
External Links:: GAMS (package FDLIBM)
Referenced by:: § ‣ Software Cross Index, § ‣ Software Cross Index.
Encodings:: BibTeX

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S. Fempl (1960) Sur certaines sommes des intégral-cosinus. Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).

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External Links:: MathReview (L. Carlitz), ZentralBlatt
Referenced by:: §6.15.
Encodings:: BibTeX

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H. E. Fettis and J. C. Caslin (1964) Tables of Elliptic Integrals of the First, Second, and Third Kind. Technical report Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.

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Notes:: Reviewed in Math. Comp. v. 1919(1965)509. Table erratum: Math. Comp. v. 20 (1966), no. 96, pp. 639-640.
Referenced by:: §19.37(ii), §19.37(ii), §19.37(iii), §19.37(iii), §19.37(iii).
Encodings:: BibTeX

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H. E. Fettis and J. C. Caslin (1969) A Table of the Complete Elliptic Integral of the First Kind for Complex Values of the Modulus. Part I. Technical report Technical Report ARL 69-0172, Aerospace Research Laboratories, Office of Aerospace Research, Wright-Patterson Air Force Base, Ohio.

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Notes:: Table erratum: Math. Comp. v. 36 (1981), no. 153, p. 318. Part II of this report, with the same date but numbered ARL 69-0173, again puts $k=R\exp(i\theta)$ but with $R$ as parameter and $\theta$ as variable instead of the other way around. Part III, dated May 1970 and numbered ARL 70-0081, contains tables of auxiliary functions to help interpolation.
External Links:: MathReview, ZentralBlatt
Referenced by:: §19.36(ii), §19.37(ii).
Encodings:: BibTeX

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G. Freud (1969) On weighted polynomial approximation on the whole real axis. Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.

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External Links:: ISSN 0001-5954, Document, Link, MathReview (A. K. Varma)
Referenced by:: §18.32.
Encodings:: BibTeX

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40: 26.5 Lattice Paths: Catalan Numbers

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Table 26.5.1: Catalan numbers.

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$n$	$C\left(n\right)$	$n$	$C\left(n\right)$	$n$	$C\left(n\right)$
…
6	132	13	7 42900	20	65641 20420

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