DLMF:13.23.E10 (Q4644)

From DRMF

Revision as of 01:03, 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:13.23.E10	No description defined

Statements

Defining formula

{\displaystyle{\displaystyle\frac{1}{\Gamma\left(1+2\mu\right)}\int_{0}^{% \infty}e^{-\frac{1}{2}t}t^{\frac{1}{2}(\nu-1)-\mu}M_{\kappa,\mu}\left(t\right)% J_{\nu}\left(2\sqrt{xt}\right)\mathrm{d}t=\frac{e^{-\frac{1}{2}x}x^{\frac{1}{2% }(\kappa+\mu-\frac{3}{2})}}{\Gamma\left(\frac{1}{2}+\mu+\kappa\right)}\*W_{% \frac{1}{2}(\kappa-3\mu+\nu+\frac{1}{2}),\frac{1}{2}(\kappa+\mu-\nu-\frac{1}{2% })}\left(x\right),}}

0 references

DLMF:13.23.E10

0 references

{\displaystyle{\displaystyle-1<\Re\nu<2\Re(\mu+\kappa)+\tfrac{1}{2}}}

0 references

{\displaystyle{\displaystyle x>0}}

0 references

{\displaystyle{\displaystyle-1<\Re\nu<2\Re(\mu+\kappa)+\tfrac{1}{2}}}

0 references

Bessel function of the first kind

Defining formula

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

C10.S2.E2.m2aadec

0 references

Defining formula

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

C5.S2.E1.m2aidec

0 references

Whittaker confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle M_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

C13.S14.E2.m2afdec

0 references

Whittaker confluent hypergeometric function

Defining formula

{\displaystyle{\displaystyle W_{\NVar{\kappa},\NVar{\mu}}\left(\NVar{z}\right)}}

C13.S14.E3.m2addec

0 references

Defining formula

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

C1.S4.SS4.m1aidec

0 references

base of natural logarithm

Defining formula

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

C4.S2.E11.m2aidec

0 references

Defining formula

{\displaystyle{\displaystyle\int}}

C1.S4.SS4.m3aidec

0 references

Defining formula

{\displaystyle{\displaystyle\Re}}

C1.S9.E2.m1aidec

0 references

Defining formula

{\displaystyle{\displaystyle x}}

C13.S1.XMD4.m1bdec

0 references

Sitelinks

Wikipedia(0 entries)

DRMF related sites(0 entries)

Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q4644&oldid=29144"