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31: Bibliography E

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The penetration of a potential barrier by electrons. Phys. Rev. 35 (11), pp. 1303–1309.

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External Links:

Document, ZentralBlatt

Referenced by:

§15.18.

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Higher Transcendental Functions. Vol. II. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 41 (1983), no. 164, p. 778, v. 36 (1981), no. 153, p. 315, v. 30 (1976), no. 135, p. 675, v. 29 (1975), no. 130, p. 670, v. 26 (1972), no. 118, p. 598, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 109, p. 239, v. 17 (1963), no. 84, p. 485.

External Links:

MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§10.22(iv), §10.22(vi), §10.23(iii), §10.23(iii), §10.23(iv), §10.32(i), §10.32(iii), §10.32(iv), §10.43(iv), §10.43(vi), §10.44(iv), §10.60(iv), §10.9(i), §10.9(iii), §10.9(iv), §11.10(vi), §11.4(i), Ch.11, §12.12, §12.12, §12.13(i), §12.5(iv), Ch.12, §18.16(vi), (18.17.21_1), §18.17(iv), §18.17(i), §18.17(viii), (18.35.1), (18.35.2), (18.35.4_5), §18.35(i), (18.5.11_1), (18.5.11_3), §18.5(ii), §18.9(iii), §19.1, §19.10(i), §19.14(ii), (19.25.40), §19.25(vi), §19.5, §19.7(ii), §19.9(i), Ch.19, §20.9(i), §22.15(ii), §23.6(iv), Ch.23, §8.13(i), §8.14, §8.3(i), §8.4, §8.6(iii), §8.7, Ch.8, Notations P, Notations P.

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Painlevé transcendent describes quantum correlation function of the $XXZ$ antiferromagnet away from the free-fermion point. J. Phys. A 29 (17), pp. 5619–5626.

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External Links:

ISSN 0305-4470, Document, MathReview (Estelle L. Basor), ZentralBlatt

Referenced by:

§32.16.

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Institutiones Calculi Integralis. Opera Omnia (1), Vol. 11, pp. 110–113.

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Referenced by:

§25.12(i).

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32: Bibliography S

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

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ISSN 0036-1410, Document, MathReview (R. K. Gupta), ZentralBlatt

Referenced by:

§29.17(i), §29.8.

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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).

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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).

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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).

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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:

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33: 2.2 Transcendental Equations

… ►Conditions for the validity of the reversion process in $ℂ$ are derived in Olver (1997b, pp. 14–16). …

34: 8.26 Tables

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

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35: 26.6 Other Lattice Path Numbers

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Table 26.6.1: Delannoy numbers $D(m,n)$.

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$m$	$n$
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1	1	3	5	7	9	11	13	15	17	19	21
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5	1	11	61	231	681	1683	3653	7183	13073	22363	36365
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Table 26.6.2: Motzkin numbers $M(n)$.

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

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Table 26.6.4: Schröder numbers $r(n)$.

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$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$	$n$	$r(n)$
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$2$	$6$	$6$	$1806$	$10$	$\mathrm{10\hspace{0.33em}37718}$	$14$	$\mathrm{7453\hspace{0.33em}87038}$	$18$	$\mathrm{60\hspace{0.33em}03188\hspace{0.33em}53926}$
$3$	$22$	$7$	$8558$	$11$	$\mathrm{52\hspace{0.33em}93446}$	$15$	$\mathrm{39376\hspace{0.33em}03038}$	$19$	$\mathrm{323\hspace{0.33em}67243\hspace{0.33em}17174}$

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36: Bibliography C

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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.

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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:

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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).

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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).

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Exact elliptic compactons in generalized Korteweg-de Vries equations. Complexity 11 (6), pp. 30–34.

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ISSN 1076-2787, Document, MathReview

Referenced by:

§19.6(i).

Encodings:

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37: Bibliography O

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Hyperasymptotic solutions of higher order linear differential equations with a singularity of rank one. Proc. Roy. Soc. London Ser. A 454, pp. 1–29.

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External Links:

ISSN 1364-5021, Document, MathReview (Donald A. Lutz), ZentralBlatt

Referenced by:

§2.11(v), §2.7(ii).

Encodings:

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Error bounds for stationary phase approximations. SIAM J. Math. Anal. 5 (1), pp. 19–29.

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Notes:

See also Olver (1997b)

External Links:

Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§2.3(iv).

Encodings:

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Numerical solution of Riemann-Hilbert problems: Painlevé II. Found. Comput. Math. 11 (2), pp. 153–179.

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External Links:

ISSN 1615-3375, Document, FullText, MathReview Entry, ZentralBlatt

Referenced by:

§32.17, §32.17.

Encodings:

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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:

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38: 26.5 Lattice Paths: Catalan Numbers

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Table 26.5.1: Catalan numbers.

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$n$	$C\left(n\right)$	$n$	$C\left(n\right)$	$n$	$C\left(n\right)$
0	1	7	429	14	26 74440
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4	14	11	58786	18	4776 38700
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39: 34.9 Graphical Method

… ►For specific examples of the graphical method of representing sums involving the $\mathit{3}j,\mathit{6}j$, and $\mathit{9}j$ symbols, see Varshalovich et al. (1988, Chapters 11, 12) and Lehman and O’Connell (1973, §3.3).

40: Richard B. Paris

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11 Struve and Related Functions

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