DLMF:4.40.E7 (Q1979)

From DRMF

Revision as of 19:22, 1 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)

(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)

Jump to navigation Jump to search

No description defined

Language	Label	Description	Also known as
English	DLMF:4.40.E7	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}e^{-x}\frac{\sin\left(ax\right)}{% \sinh x}\mathrm{d}x=\tfrac{1}{2}\pi\coth\left(\tfrac{1}{2}\pi a\right)-\frac{1% }{a},}}

0 references

DLMF:4.40.E7

0 references

{\displaystyle{\displaystyle a\neq 0}}

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.m1afdec

0 references

base of natural logarithm

Defining formula

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

C4.S2.E11.m2adec

0 references

hyperbolic cotangent function

Defining formula

{\displaystyle{\displaystyle\coth\NVar{z}}}

C4.S28.E7.m2aadec

0 references

hyperbolic sine function

Defining formula

{\displaystyle{\displaystyle\sinh\NVar{z}}}

C4.S28.E1.m2acdec

0 references

Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3afdec

0 references

Defining formula

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

C4.S14.E1.m2adec

0 references

Defining formula

{\displaystyle{\displaystyle a}}

C4.S1.XMD4.m1dec

0 references

Defining formula

{\displaystyle{\displaystyle x}}

C4.S1.XMD6.m1fdec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q1979&oldid=28298"