2022年福彩3D历史上的今天开奖号085期【杏彩官方qee9.com】yGfq2Nne

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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: 27.11 Asymptotic Formulas: Partial Sums

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27.11.2 $$\sum _{n\le x}d\left(n\right)=x\ln x+(2\gamma -1)x+O\left(\sqrt{x}\right),$$

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Symbols:

$O\left(x\right)$: order not exceeding, $\gamma$: Euler’s constant, $d_k\left(n\right)$: divisor function, $\ln z$: principal branch of logarithm function, $n$: positive integer and $x$: real number

A&S Ref:

24.3.3 III

Referenced by:

§27.11, §27.11, Erratum (V1.1.8) for Section 27.11

Permalink:

http://dlmf.nist.gov/27.11.E2

Encodings:

pMML, png, TeX

Change of Notation (effective with 1.0.10):

The notation for logarithm has been changed to $\ln$ from $\log$.

See also:

Annotations for §27.11 and Ch.27

… ►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 $\theta >{\theta }_0$. … ►

27.11.3 $$\sum _{n\le x}\frac{d\left(n\right)}{n}=\frac{1}{2}{(\ln x)}^2+2\gamma \ln x+O\left(1\right),$$

ⓘ

Symbols:

$O\left(x\right)$: order not exceeding, $\gamma$: Euler’s constant, $d_k\left(n\right)$: divisor function, $\ln z$: principal branch of logarithm function, $n$: positive integer and $x$: real number

Referenced by:

§27.11

Permalink:

http://dlmf.nist.gov/27.11.E3

Encodings:

pMML, png, TeX

Change of Notation (effective with 1.0.10):

The notation for logarithm has been changed to $\ln$ from $\log$.

See also:

Annotations for §27.11 and Ch.27

…

7: 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

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8: Errata

… ►

Version 1.1.8 (December 15, 2022)

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Version 1.1.7 (October 15, 2022)

… ►

Version 1.1.6 (June 30, 2022)

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Version 1.1.5 (March 15, 2022)

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Version 1.1.4 (January 15, 2022)

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9: 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).

10: 8.18 Asymptotic Expansions of $I_x(a,b)$

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