Abstract
This paper introduces and studies a generalization of the classical Struve function of order p given by S-a(p,c)(x) :=Sigma(infinity)(k=0) (-c)(k)/Gamma(ak+p+3/2) Gamma(k+3/2) (x/2)(2k+p+1) .
Representation formulae are derived for a S p, c. Further the function S-a(p,c) is shown to be a solution of an (a + 1)-order differential equation. Monotonicity and log-convexity properties for the generalized Struve function S-a(p,c) are investigated, particulary for the case c = -1. As a consequence, Turan-type inequalities are established. For a = 2 and c = -1, dominant and subordinant functions are obtained for the Struve function S-2(p),-1.