布雷西亚桑塔朱利亚美术学院学历认证【假证加微aptao168】choi

SearchAdvancedHelp

Your search matched, but the results seem poor.

The terms "学院学", "aptao168" were not found.Possible alternative terms: "choic", "caption".

See Search Help for suggestions.

(0.001 seconds)

8 matching pages

1: 16.6 Transformations of Variable

… ►For Kummer-type transformations of ${}_2{}^{}F_2^{}$ functions see Miller (2003) and Paris (2005a), and for further transformations see Erdélyi et al. (1953a, §4.5), Miller and Paris (2011), Choi and Rathie (2013) and Wang and Rathie (2013).

2: 25.8 Sums

… ►

25.8.9 $$\sum _{k=1}^{\mathrm{\infty }}\frac{\zeta \left(2k\right)}{(2k+1)2^{2k}}=\frac{1}{2}-\frac{1}{2}\ln 2.$$

ⓘ

Symbols:

$\zeta \left(s\right)$: Riemann zeta function, $\ln z$: principal branch of logarithm function and $k$: nonnegative integer

Keywords:

infinite series

Source:

Srivastava and Choi (2001, (467), p. 212)

Permalink:

http://dlmf.nist.gov/25.8.E9

Encodings:

pMML, png, TeX

See also:

Annotations for §25.8 and Ch.25

… ►For other sums see Prudnikov et al. (1986b, pp. 648–649), Hansen (1975, pp. 355–357), Ogreid and Osland (1998), and Srivastava and Choi (2001, Chapter 3).

3: 25.11 Hurwitz Zeta Function

… ►

25.11.8 $$\zeta (s,\frac{1}{2}a)=\zeta (s,\frac{1}{2}a+\frac{1}{2})+2^s\sum _{n=0}^{\mathrm{\infty }}\frac{{(-1)}^n}{{(n+a)}^s},$$ $\mathrm{\Re }s>0$, $s\ne 1$, .

ⓘ

Symbols:

$\zeta (s,a)$: Hurwitz zeta function, $\mathrm{\Re }$: real part, $n$: nonnegative integer, $a$: real or complex parameter and $s$: complex variable

Keywords:

infinite series, series representation

Source:

Srivastava and Choi (2001, (5), p. 89)

Referenced by:

(25.11.35), §25.11(x)

Permalink:

http://dlmf.nist.gov/25.11.E8

Encodings:

pMML, png, TeX

See also:

Annotations for §25.11(iv), §25.11 and Ch.25

… ►

25.11.25 $$\zeta (s,a)=\frac{1}{\mathrm{\Gamma }\left(s\right)}{\int }_0^{\mathrm{\infty }}\frac{x^{s-1}{\mathrm{e}}^{-ax}}{1-{\mathrm{e}}^{-x}}dx,$$ $\mathrm{\Re }s>1$, $\mathrm{\Re }a>0$.

ⓘ

Symbols:

$\mathrm{\Gamma }\left(z\right)$: gamma function, $\zeta (s,a)$: Hurwitz zeta function, $dx$: differential of $x$ , $\mathrm{e}$: base of natural logarithm, $\int$: integral, $\mathrm{\Re }$: real part, $x$: real variable, $a$: real or complex parameter and $s$: complex variable

Keywords:

improper integral, integral representation

Sources:

Srivastava and Choi (2001, (2), p. 89); Apostol (1976, (5), p. 251)

Referenced by:

(25.11.27), (25.11.30), (25.11.35), §25.11(x)

Permalink:

http://dlmf.nist.gov/25.11.E25

Encodings:

pMML, png, TeX

See also:

Annotations for §25.11(vii), §25.11 and Ch.25

… ►See also (8.15.2) and Srivastava and Choi (2001). …

4: Bibliography N

… ►

Error bounds and exponential improvement for Hermite’s asymptotic expansion for the gamma function. Appl. Anal. Discrete Math. 7 (1), pp. 161–179.

ⓘ

External Links:

ISSN 1452-8630, Document, FullText, MathReview (Junesang Choi), ZentralBlatt

Referenced by:

§5.11(ii), §5.11(ii).

Encodings:

BibTeX

…

5: Bibliography C

… ►

An extension of a Kummer’s quadratic transformation formula with an application. Proc. Jangjeon Math. Soc. 16 (2), pp. 229–235.

ⓘ

External Links:

ISSN 1598-7264, MathReview (Petr Blaschke), ZentralBlatt

Referenced by:

§16.6, §16.6.

Encodings:

BibTeX

…

6: Bibliography S

… ►

Series Associated with the Zeta and Related Functions. Kluwer Academic Publishers, Dordrecht.

ⓘ

External Links:

ISBN 0-7923-7054-6, MathReview (Richard B. Paris), ZentralBlatt

Referenced by:

(25.11.25), (25.11.8), §25.11, §25.11(iv), §25.11(x), (25.8.9), §25.8.

Encodings:

BibTeX

…

7: Bibliography

… ►

Gamma function inequalities. Numer. Algorithms 49 (1-4), pp. 53–84.

ⓘ

External Links:

ISSN 1017-1398, Document, FullText, MathReview (Junesang Choi), ZentralBlatt

Referenced by:

§5.6(i), §5.6(i).

Encodings:

BibTeX

…

8: Bibliography L

… ►

New method to obtain small parameter power series expansions of Mathieu radial and angular functions. Math. Comp. 78 (265), pp. 255–274.

ⓘ

External Links:

ISSN 0025-5718, Document, FullText, MathReview (Junesang Choi), ZentralBlatt

Referenced by:

§28.24, §28.24.

Encodings:

BibTeX

…