DLMF:10.22.E67 (Q3441)

From DRMF

Revision as of 13:26, 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.E67	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\int_{0}^{\infty}t\exp\left(-p^{2}t^{2}\right)J_{% \nu}\left(at\right)J_{\nu}\left(bt\right)\mathrm{d}t=\frac{1}{2p^{2}}\exp\left% (-\frac{a^{2}+b^{2}}{4p^{2}}\right)I_{\nu}\left(\frac{ab}{2p^{2}}\right),}}

0 references

DLMF:10.22.E67

0 references

{\displaystyle{\displaystyle\Re\nu>-1,\Re(p^{2})>0}}

0 references

Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aazdec

0 references

Defining formula

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

C1.S4.SS4.m1abndec

0 references

exponential function

Defining formula

{\displaystyle{\displaystyle\exp\NVar{z}}}

C4.S2.E19.m2afdec

0 references

Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3abndec

0 references

modified Bessel function of the first kind

Defining formula

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

C10.S25.E2.m2acdec

0 references

Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aandec

0 references

Defining formula

{\displaystyle{\displaystyle\nu}}

C10.S1.XMD7.m1atdec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3441&oldid=36514"