![int_0^inftyJ_mu(at)J_nu(bt)t^(-lambda)dt=(a^muGamma[(mu+nu-lambda+1)/2])/(2^lambdab^(mu-lambda+1)Gamma[(-mu+nu+lambda+1)/2]Gamma(mu+1))
×_2F_1((mu+nu-lambda+1)/2,(mu-nu-lambda+1)/2;mu+1;a^2/b^2),](/images/equations/Sonine-SchafheitlinFormula/NumberedEquation1.svg) |
where ![R[mu+nu-lambda+1]>0](/images/equations/Sonine-SchafheitlinFormula/Inline1.svg)
,
![R[lambda]>-1](/images/equations/Sonine-SchafheitlinFormula/Inline2.svg)
,
,
is a Bessel function of the first kind,
is the gamma function, and 
is a hypergeometric
function.
Sonine-Schafheitlin Formula
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References
Iyanaga, S. and Kawada, Y. (Eds.). Encyclopedic Dictionary of Mathematics. Cambridge, MA: MIT Press, p. 1474, 1980.Referenced on Wolfram|Alpha
Sonine-Schafheitlin FormulaCite this as:
Weisstein, Eric W. "Sonine-Schafheitlin Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Sonine-SchafheitlinFormula.html