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1: 11 Struve and Related Functions

Chapter 11 Struve and Related Functions

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2: 13.30 Tables

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Slater (1960) tabulates $M(a,b,x)$ for $a=-1(.1)1$, $b=0.1(.1)1$, and $x=0.1(.1)10$, 7–9S; $M(a,b,1)$ for $a=-11(.2)2$ and $b=-4(.2)1$, 7D; the smallest positive $x$-zero of $M(a,b,x)$ for $a=-4(.1)-0.1$ and $b=0.1(.1)2.5$, 7D.

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Abramowitz and Stegun (1964, Chapter 13) tabulates $M(a,b,x)$ for $a=-1(.1)1$, $b=0.1(.1)1$, and $x=0.1(.1)1(1)10$, 8S. Also the smallest positive $x$-zero of $M(a,b,x)$ for $a=-1(.1)-0.1$ and $b=0.1(.1)1$, 7D.

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

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3: 24.2 Definitions and Generating Functions

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Table 24.2.4: Euler numbers $E_n$.

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$n$	$E_n$
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$30$	$-\mathrm{44\hspace{0.33em}15438\hspace{0.33em}93249\hspace{0.33em}02310\hspace{0.33em}45536\hspace{0.33em}82821}$
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Table 24.2.5: Coefficients $b_{n,k}$ of the Bernoulli polynomials $B_n\left(x\right)={\sum }_{k=0}^n{b}_{n,k}{x}^k$.

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	$k$
$n$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
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$11$	$0$	$\frac{5}{6}$	$0$	$-\frac{11}{2}$	$0$	$11$	$0$	$-11$	$0$	$\frac{55}{6}$	$-\frac{11}{2}$	$1$
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Table 24.2.6: Coefficients $e_{n,k}$ of the Euler polynomials $E_n\left(x\right)={\sum }_{k=0}^n{e}_{n,k}{x}^k$.

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	$k$
$n$	$0$	$1$	$2$	$3$	$4$	$5$	$6$	$7$	$8$	$9$	$10$	$11$	$12$	$13$	$14$	$15$
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$10$	$0$	$-155$	$0$	$255$	$0$	$-126$	$0$	$30$	$0$	$-5$	$1$
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4: Staff

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Leonard C. Maximon, George Washington University, Chaps. 10, 34

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Richard B. Paris, University of Abertay, Chaps. 8, 11

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Hans Volkmer, University of Wisconsin, Milwaukee, Chaps. 29, 30

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Richard B. Paris, University of Abertay Dundee, for Chaps. 8, 11 (deceased)

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Hans Volkmer, University of Wisconsin–Milwaukee, for Chaps. 29, 30

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5: 8.26 Tables

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Zhang and Jin (1996, Table 3.8) tabulates $\gamma (a,x)$ for $a=0.5,1,3,5,10,25,50,100$, $x=0(.1)1(1)3,5(5)30,50,100$ to 8D or 8S.

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Pearson (1968) tabulates $I_x(a,b)$ for $x=0.01(.01)1$, $a,b=0.5(.5)11(1)50$, with $b\le a$, to 7D.

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Zhang and Jin (1996, Table 3.9) tabulates $I_x(a,b)$ for $x=0(.05)1$, $a=0.5,1,3,5,10$, $b=1,10$ to 8D.

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Stankiewicz (1968) tabulates $E_n\left(x\right)$ for $n=1(1)10$, $x=0.01(.01)5$ to 7D.

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Zhang and Jin (1996, Table 19.1) tabulates $E_n\left(x\right)$ for $n=1,2,3,5,10,15,20$, $x=0(.1)1,1.5,2,3,5,10,20,30,50,100$ to 7D or 8S.

6: 26.2 Basic Definitions

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Table 26.2.1: Partitions $p\left(n\right)$.

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$n$	$p\left(n\right)$	$n$	$p\left(n\right)$	$n$	$p\left(n\right)$
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6	11	23	1255	40	37338
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9	30	26	2436	43	63261
10	42	27	3010	44	75175
11	56	28	3718	45	89134
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13	101	30	5604	47	1 24754
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7: 26.9 Integer Partitions: Restricted Number and Part Size

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Table 26.9.1: Partitions $p_k\left(n\right)$.

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$n$	$k$
	0	1	2	3	4	5	6	7	8	9	10
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6	0	1	4	7	9	10	11	11	11	11	11
7	0	1	4	8	11	13	14	15	15	15	15
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9	0	1	5	12	18	23	26	28	29	30	30
10	0	1	6	14	23	30	35	38	40	41	42

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8: 6.19 Tables

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Abramowitz and Stegun (1964, Chapter 5) includes $x^{-1}\mathrm{Si}\left(x\right)$, $-x^{-2}\mathrm{Cin}\left(x\right)$, $x^{-1}\mathrm{Ein}\left(x\right)$, $-x^{-1}\mathrm{Ein}\left(-x\right)$, $x=0(.01)0.5$; $\mathrm{Si}\left(x\right)$, $\mathrm{Ci}\left(x\right)$, $\mathrm{Ei}\left(x\right)$, $E_1\left(x\right)$, $x=0.5(.01)2$; $\mathrm{Si}\left(x\right)$, $\mathrm{Ci}\left(x\right)$, $x{\mathrm{e}}^{-x}\mathrm{Ei}\left(x\right)$, $x{\mathrm{e}}^x{E}_1\left(x\right)$, $x=2(.1)10$; $x\mathrm{f}\left(x\right)$, $x^2\mathrm{g}\left(x\right)$, $x{\mathrm{e}}^{-x}\mathrm{Ei}\left(x\right)$, $x{\mathrm{e}}^x{E}_1\left(x\right)$, $x^{-1}=0(.005)0.1$; $\mathrm{Si}\left(\pi x\right)$, $\mathrm{Cin}\left(\pi x\right)$, $x=0(.1)10$. Accuracy varies but is within the range 8S–11S.

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Zhang and Jin (1996, pp. 652, 689) includes $\mathrm{Si}\left(x\right)$, $\mathrm{Ci}\left(x\right)$, $x=0(.5)20(2)30$, 8D; $\mathrm{Ei}\left(x\right)$, $E_1\left(x\right)$, $x=[0,100]$, 8S.

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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.

9: Publications

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Boundary/Contour Fitted Grid Generation for Effective Visualizations in a Digital Library of Mathematical Functions, Proceedings of the 9th International Conference on Numerical Grid Generation in Computational Field Simulations, San Jose, June 11–18, 2005. pp. 61–71.

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Web-Based 3D Visualization in a Digital Library of Mathematical Functions, Proceedings of the Web3D Symposium, Bangor, UK, March 29–April 1, 2005.

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Methods of Relevance Ranking and Hit-content Generation in Math Search, Proceedings of Mathematical Knowledge Management (MKM2007), RISC, Hagenberg, Austria, June 27–30, 2007.

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10: 10 Bessel Functions

Chapter 10 Bessel Functions

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