DLMF:10.22.E71 (Q3445): Difference between revisions

From DRMF

Jump to navigation Jump to search

Latest revision as of 13:27, 2 January 2020

No description defined

Language	Label	Description	Also known as
English	DLMF:10.22.E71	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}J_{\mu}\left(at\right)J_{\nu}% \left(bt\right)J_{\nu}\left(ct\right)t^{1-\mu}\mathrm{d}t=\frac{(bc)^{\mu-1}(% \sin\phi)^{\mu-\frac{1}{2}}}{(2\pi)^{\frac{1}{2}}a^{\mu}}\mathsf{P}^{\frac{1}{% 2}-\mu}_{\nu-\frac{1}{2}}(\cos\phi),}}

0 references

DLMF:10.22.E71

0 references

{\displaystyle{\displaystyle\Re\mu>-\tfrac{1}{2},\Re\nu>-1,|b-c|<a<b+c,\cos% \phi=(b^{2}+c^{2}-a^{2})/(2bc)}}

0 references

Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2abddec

0 references

Ferrers function of the first kind

Defining formula

{\displaystyle{\displaystyle\mathsf{P}^{\NVar{\mu}}_{\NVar{\nu}}\left(\NVar{x}% \right)}}

C14.S3.E1.m2adec

0 references

the ratio of the circumference of a circle to its diameter

Defining formula

{\displaystyle{\displaystyle\pi}}

C3.S12.E1.m2aacdec

0 references

cosine function

Defining formula

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

C4.S14.E2.m2andec

0 references

Defining formula

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

C1.S4.SS4.m1abrdec

0 references

Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abrdec

0 references

Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aardec

0 references

Defining formula

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

C4.S14.E1.m2andec

0 references

Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1awdec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3445&oldid=36690"