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    Multivariable confluence hypergeometric function

    I'm looking for any kind of reference on a multivariable generalization of a (confluent) hypergeometric function. In particular, Horns list is a list of 34 two-variable hypergeometric functions, 20 of which are confluent. Then one of these has the following series expansion: \Phi_2(\beta...
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    Series of a Bessel function

    In solving a particular kind of integral I ended up with the following series \sum_{k=0}^\infty \frac{\Gamma[b+k]}{\Gamma[a+b+k]} \frac{(1-t^2)^k}{k!} \left(\frac{\omega}{2}\right)^k J_{a+b-\frac{1}{2} +k} (\omega) where 0<t<1, and a,b are small and positive. I tried looking it up in a...