For ![R[mu+nu]>0](/images/equations/Weber-SonineFormula/Inline1.svg)
,
,
and 
,
![int_0^inftyJ_nu(at)e^(-p^2t^2)t^(mu-1)dt=(a/(2p))^nu(Gamma[1/2(nu+mu)])/(2p^muGamma(nu+1))_1F_1(1/2(nu+mu);nu+1;-(a^2)/(4p^2)),](/images/equations/Weber-SonineFormula/NumberedEquation1.svg) |
where 
is a Bessel function of the first kind,
is the gamma function, and 
is a confluent
hypergeometric function of the first kind.
Weber-Sonine Formula
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References
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1474, 1980.Watson, G. N. A Treatise on the Theory of Bessel Functions, 2nd ed. Cambridge, England: Cambridge University Press, p. 393, 1966.Referenced on Wolfram|Alpha
Weber-Sonine FormulaCite this as:
Weisstein, Eric W. "Weber-Sonine Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Weber-SonineFormula.html