DLMF:25.14.E6 (Q7745): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit Newer edit →

Revision as of 01:03, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:25.14.E6	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\Phi\left(z,s,a\right)=\frac{1}{2}a^{-s}+\int_{0}^% {\infty}\frac{z^{x}}{(a+x)^{s}}\mathrm{d}x-2\int_{0}^{\infty}\frac{\sin\left(x% \ln z-s\operatorname{arctan}\left(x/a\right)\right)}{(a^{2}+x^{2})^{s/2}(e^{2% \pi x}-1)}\mathrm{d}x,}}

0 references

DLMF:25.14.E6

0 references

{\displaystyle{\displaystyle\Re s>0}}

0 references

{\displaystyle{\displaystyle\Re s>1}}

0 references

{\displaystyle{\displaystyle|z|=1,\Re a>0}}

0 references

{\displaystyle{\displaystyle\Re s>0}}

0 references

{\displaystyle{\displaystyle|z|<1}}

0 references

{\displaystyle{\displaystyle\Re s>1}}

0 references

{\displaystyle{\displaystyle|z|=1,\Re a>0}}

0 references

Lerch’s transcendent

Defining formula

{\displaystyle{\displaystyle\Phi\left(\NVar{z},\NVar{s},\NVar{a}\right)}}

C25.S14.E1.m2aedec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

C1.S4.SS4.m1aadec

0 references

base of natural logarithm

Defining formula

{\displaystyle{\displaystyle\mathrm{e}}}

C4.S2.E11.m2aadec

0 references

Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aadec

0 references

Defining formula

{\displaystyle{\displaystyle\operatorname{arctan}\NVar{z}}}

C4.S23.SS2.p1.m7adec

0 references

principal branch of logarithm function

Defining formula

{\displaystyle{\displaystyle\ln\NVar{z}}}

C4.S2.E2.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1addec

0 references

Defining formula

{\displaystyle{\displaystyle\sin\NVar{z}}}

C4.S14.E1.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle x}}

C25.S1.XMD5.m1adec

0 references

Defining formula

{\displaystyle{\displaystyle a}}

C25.S1.XMD6.m1ddec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q7745&oldid=29141"