Differentiation of special functions with respect to parameters

Yury 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).