
Differentiation of special functions with respect to parametersYury Brychkov
Derivatives with respect to order v are known for the Bessel functions J(v,z}, I(v,z), K(v,z) at the points v=+n and v=+1/2, +3/2 (see W.Magnus, F.Oberhettinger, R.P.Soni, ``Formulas and theorems for the special functions of mathematical physics'', Springer, 1966) and for Struve functions H(v,z), L(v,z) at the points v=+1/2. We give closed forms of derivatives for these functions and for integral Bessel functions at the points v=+n, +n+1/2, where n=0,1,.... Using these results some classes of derivatives with respect to parameters are found for the Gauss and generalized hypergeometric functions. These formulas can be used, in particular, for evaluation of integrals involving the logarithmic function (SCG Integration Project). 