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1: Bibliography U

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On the transformation group of the second Painlevé equation. Nagoya Math. J. 157, pp. 15–46.

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External Links:

ISSN 0027-7630, MathReview (Andrei A. Kapaev), ZentralBlatt

Referenced by:

§32.7(viii).

Encodings:

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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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External Links:

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

Referenced by:

§24.16(iii).

Encodings:

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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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External Links:

Document, MathReview (L. Berg), ZentralBlatt

Referenced by:

§36.12(iii).

Encodings:

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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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External Links:

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

Referenced by:

§36.12(iii).

Encodings:

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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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External Links:

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

Referenced by:

§14.26.

Encodings:

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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

… ►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 $z$

… ►When the foregoing results are combined with Kummer’s transformation (13.2.39), an approximation is obtained for the case when $|b|$ is large, and $|b-a|$ and $|z|$ are bounded. ►

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

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§13.8(iv) Large $a$ and $b$

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5: 13.9 Zeros

… ►For fixed $a,b\in ℂ$ the large $z$-zeros of $M(a,b,z)$ satisfy … ►For fixed $b$ and $z$ in $ℂ$ the large $a$-zeros of $M(a,b,z)$ are given by … ►For fixed $b$ and $z$ in $ℂ$ the large $a$-zeros of $U(a,b,z)$ are given by …

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

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External Links:

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

Referenced by:

§15.12(iii), §15.12(iii).

Encodings:

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