DLMF:10.22.E23 (Q3397)

From DRMF

Revision as of 01:17, 2 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:10.22.E23	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\frac{1}{2}\pi}J_{\mu}\left(z{\sin^{2}}% \theta\right)J_{\nu}\left(z{\cos^{2}}\theta\right)(\sin\theta)^{2\alpha-1}\sec% \theta\mathrm{d}\theta=\frac{(\mu+\nu+\alpha)\Gamma\left(\mu+\alpha\right)2^{% \alpha-1}}{\nu\Gamma\left(\mu+1\right)z^{\alpha}}J_{\mu+\nu+\alpha}\left(z% \right),}}

0 references

DLMF:10.22.E23

0 references

{\displaystyle{\displaystyle\Re(\mu+\alpha)>0}}

0 references

{\displaystyle{\displaystyle\Re\nu>0}}

0 references

Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aodec

0 references

Defining formula

{\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}

C5.S2.E1.m2afdec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2akdec

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.m1avdec

0 references

Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3avdec

0 references

Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1ajdec

0 references

secant function

Defining formula

{\displaystyle{\displaystyle\sec\NVar{z}}}

C4.S14.E6.m2adec

0 references

Defining formula

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

C4.S14.E1.m2ahdec

0 references

Defining formula

{\displaystyle{\displaystyle z}}

C10.S1.XMD6.m1qdec

0 references

Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1mdec

0 references

Defining formula

{\displaystyle{\displaystyle\alpha}}

C10.S22.XMD1.m1dec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3397&oldid=30200"