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1: Gergő Nemes

… ►In March 2022, Nemes was named Contributing Developer of the NIST Digital Library of Mathematical Functions.

2: Wolter Groenevelt

… ►As of September 20, 2022, Groenevelt performed a complete analysis and acted as main consultant for the update of the source citation and proof metadata for every formula in Chapter 18 Orthogonal Polynomials. …

3: Richard B. Paris

… ► 2022) was Reader in Mathematics at the University of Abertay Dundee, U. …

4: Diego Dominici

… ►He was elected as Program Director for the period 2011–2016 and served as OPSF-Talk moderator from 2010–2022 with Bonita Saunders, and co-editor for OPSF-Net from 2006–2015 with Martin Muldoon. …

5: DLMF Project News

error generating summary

6: Bibliography T

… ►

Asymptotic expansions of Kummer hypergeometric functions with three asymptotic parameters a, b and z. Indagationes Mathematicae.

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External Links:

ISSN 0019-3577, Document, Link

Referenced by:

§13.8(iv).

Encodings:

BibTeX

… ►

Asymptotic expansions of Kummer hypergeometric functions for large values of the parameters. Integral Transforms Spec. Funct. 33 (1), pp. 16–31.

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External Links:

ISSN 1065-2469, Document, Link, MathReview Entry, ZentralBlatt

Referenced by:

§13.8(iv).

Encodings:

BibTeX

…

7: 13.8 Asymptotic Approximations for Large Parameters

… ►These results follow from Temme (2022), which can also be used to obtain more terms in the expansions. For generalizations in which $z$ is also allowed to be large see Temme and Veling (2022).

8: 8.18 Asymptotic Expansions of $I_x(a,b)$

… ►If $b$ and $x$ are fixed, with $b>0$ and , then as $a\to \mathrm{\infty }$ …for each $n=0,1,2,\mathrm{\dots }$. … ►If $b\to \mathrm{\infty }$ and $a$ and $x$ are fixed, with $a>0$ and , then (8.18.1), with $a$ and $b$ interchanged and $x$ replaced by $1-x$, can be combined with (8.17.4). … ►uniformly for $x\in (0,1]$. … ►uniformly for $b\in (0,\mathrm{\infty })$ and $x\in (0,1)$. …

9: 27.11 Asymptotic Formulas: Partial Sums

… ►Dirichlet’s divisor problem (unsolved as of 2022) is to determine the least number ${\theta }_0$ such that the error term in (27.11.2) is $O\left(x^{\theta }\right)$ for all $\theta >{\theta }_0$. …

10: Bibliography N

… ►

Mémoire sur les polynomes de Bernoulli. Acta Math. 43, pp. 121–196 (French).

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External Links:

Document, ZentralBlatt

Referenced by:

§24.13(i), §24.13(ii), §24.14(i), Ch.24.

Encodings:

BibTeX

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