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1: Bibliography U

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On the equation $f(1)1^k+f(2)2^k+\mathrm{\cdots }+f(x)x^k+R(x)=B{y}^2$ . Acta Arith. 51 (4), pp. 349–368.

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ISSN 0065-1036, Pdf, MathReview (István Gaál), ZentralBlatt

Referenced by:

§24.16(iii).

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Integrals with a large parameter. Several nearly coincident saddle-points. Proc. Cambridge Philos. Soc. 72, pp. 49–65.

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Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§36.12(iii).

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Integrals with a large parameter: A double complex integral with four nearly coincident saddle-points. Math. Proc. Cambridge Philos. Soc. 87 (2), pp. 249–273.

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ISSN 0305-0041, Document, MathReview (F. I. Ibragimov), ZentralBlatt

Referenced by:

§36.12(iii).

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Integrals with a large parameter: Legendre functions of large degree and fixed order. Math. Proc. Cambridge Philos. Soc. 95 (2), pp. 367–380.

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ISSN 0305-0041, Document, MathReview (Roderick Wong), ZentralBlatt

Referenced by:

§14.26.

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2: Karl Dilcher

… ►Karl Dilcher (b. … ►Over the years he authored or coauthored numerous papers on Bernoulli numbers and related topics, and he maintains a large on-line bibliography on the subject. …

3: 15.12 Asymptotic Approximations

… ►For large $b$ and $c$ with $c>b+1$ see López and Pagola (2011). … ►If , then as $\lambda \to \mathrm{\infty }$ with $|\mathrm{ph}\lambda |\le \pi -\delta$, … ►If , then as $\lambda \to \mathrm{\infty }$ with $|\mathrm{ph}\lambda |\le \pi -\delta$, … ►If , then as $\lambda \to \mathrm{\infty }$ with $|\mathrm{ph}\lambda |\le \frac{1}{2}\pi -\delta$, … ►For other extensions, see Wagner (1986), Temme (2003) and Temme (2015, Chapters 12 and 28).

4: 13.8 Asymptotic Approximations for Large Parameters

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§13.8(i) Large $|b|$, Fixed $a$ and $z$

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§13.8(ii) Large $b$ and $z$, Fixed $a$ and $b/z$

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§13.8(iii) Large $a$

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§13.8(iv) Large $a$ and $b$

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5: 13.9 Zeros

… ►where $n$ is a large positive integer, and the logarithm takes its principal value (§4.2(i)). … ►For fixed $b$ and $z$ in $ℂ$ the large $a$-zeros of $M(a,b,z)$ are given by …where $n$ is a large positive integer. … ►For fixed $b$ and $z$ in $ℂ$ the large $a$-zeros of $U(a,b,z)$ are given by …where $n$ is a large positive integer. …

6: 8.11 Asymptotic Approximations and Expansions

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§8.11(i) Large $z$, Fixed $a$

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§8.11(ii) Large $a$, Fixed $z$

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§8.11(iii) Large $a$, Fixed $z/a$

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§8.11(iv) Large $a$, Bounded $(x-a)/{(2a)}^{\frac{1}{2}}$

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7: 15.19 Methods of Computation

… ►Large values of $|a|$ or $|b|$, for example, delay convergence of the Gauss series, and may also lead to severe cancellation. ►For fast computation of $F(a,b;c;z)$ with $a,b$ and $c$ complex, and with application to Pöschl–Teller–Ginocchio potential wave functions, see Michel and Stoitsov (2008). … ►The relations in §15.5(ii) can be used to compute $F(a,b;c;z)$, provided that care is taken to apply these relations in a stable manner; see §3.6(ii). Initial values for moderate values of $|a|$ and $|b|$ can be obtained by the methods of §15.19(i), and for large values of $|a|$, $|b|$, or $|c|$ via the asymptotic expansions of §§15.12(ii) and 15.12(iii). ►For example, in the half-plane $\mathrm{\Re }z\le \frac{1}{2}$ we can use (15.12.2) or (15.12.3) to compute $F(a,b;c+N+1;z)$ and $F(a,b;c+N;z)$, where $N$ is a large positive integer, and then apply (15.5.18) in the backward direction. …

8: 16.22 Asymptotic Expansions

… ►Asymptotic expansions of $G_{p,q}^{m,n}(z;𝐚;𝐛)$ for large $z$ are given in Luke (1969a, §§5.7 and 5.10) and Luke (1975, §5.9). …

9: Preface

… ►Bickel, B. …Eberhardt, B. … B. … B. …Undoubtedly, the editors have overlooked some individuals who contributed, as is inevitable in a large long-lasting project. …

10: Bibliography F

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Algorithms and codes for the Macdonald function: Recent progress and comparisons. J. Comput. Appl. Math. 161 (1), pp. 179–192.

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External Links:

ISSN 0377-0427, MathReview (Boro Döring), ZentralBlatt

Referenced by:

§10.77(vi).

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Uniform asymptotic expansions for hypergeometric functions with large parameters IV. Anal. Appl. (Singap.) 12 (6), pp. 667–710.

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ISSN 0219-5305, Document, Link, MathReview (Javier Segura), ZentralBlatt

Referenced by:

§15.12(iii), §15.12(iii).

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On the reciprocal modulus relation for elliptic integrals. SIAM J. Math. Anal. 1 (4), pp. 524–526.

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Document, MathReview (B. C. Carlson), ZentralBlatt

Referenced by:

§19.7(i).

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Uniform asymptotic expansions of certain classes of Meijer $G$-functions for a large parameter. SIAM J. Math. Anal. 4 (3), pp. 482–507.

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Document, MathReview (C. M. Joshi), ZentralBlatt

Referenced by:

§16.22.

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Uniform asymptotic expansions of a class of Meijer $G$-functions for a large parameter. SIAM J. Math. Anal. 14 (6), pp. 1204–1253.

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ISSN 0036-1410, Document, MathReview (Roop N. Kesarwani), ZentralBlatt

Referenced by:

§16.22.

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