DLMF:10.9.E13 (Q3081): Difference between revisions

From DRMF

Jump to navigation Jump to search

← Older edit Newer edit →

Revision as of 15:14, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.9.E13	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\left(\frac{z+\zeta}{z-\zeta}\right)^{\frac{1}{2}% \nu}J_{\nu}\left((z^{2}-\zeta^{2})^{\frac{1}{2}}\right)=\frac{1}{\pi}\int_{0}^% {\pi}e^{\zeta\cos\theta}\cos\left(z\sin\theta-\nu\theta\right)\mathrm{d}\theta% -\frac{\sin\left(\nu\pi\right)}{\pi}\int_{0}^{\infty}e^{-\zeta\cosh t-z\sinh t% -\nu t}\mathrm{d}t,}}

0 references

DLMF:10.9.E13

0 references

{\displaystyle{\displaystyle\Re(z+\zeta)>0}}

0 references

Bessel function of the first kind

Defining formula

{\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}

C10.S2.E2.m2agdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aldec

0 references

cosine function

Defining formula

{\displaystyle{\displaystyle\cos\NVar{z}}}

C4.S14.E2.m2aidec

0 references

Defining formula

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

C1.S4.SS4.m1aldec

0 references

base of natural logarithm

Defining formula

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

C4.S2.E11.m2afdec

0 references

hyperbolic cosine function

Defining formula

{\displaystyle{\displaystyle\cosh\NVar{z}}}

C4.S28.E2.m2addec

0 references

hyperbolic sine function

Defining formula

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

C4.S28.E1.m2abdec

0 references

Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aldec

0 references

Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1addec

0 references

Defining formula

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

C4.S14.E1.m2ajdec

0 references

Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1idec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3081&oldid=55649"