Integro-differential equations and generalized hypergeometric functions

[摘要] This paper is concerned with the integro-differential equations p'(t) = ay(t) + integral(0)(1) y(qt) d mu(q) + integral(0)(1) y'(qt) d nu(q) and y(t) + integral(0)(1) y(qt) d mu(q) + integral(0)(1) y'(qt) d nu(q) = 0, where a is a complex constant, and mu and nu are complex-valued functions of bounded variation on [0, 1]. The main motivation is that the generalized hypergeometric function F-A(B)(alpha(1),...,alpha(A); beta(1),...,beta(B); t) satisfies the first equation when A less than or equal to B and the second equation when A = B + 1 for appropriately chosen constant a and smooth functions mu and nu. The first equation also includes as a special case the well-known pantograph equation and many of its generalisations. The main objects of this paper are well-posedness of initial value problems, Dirichlet and Dirichlet-Taylor series expansions, and asymptotic behaviour of the solutions. (C) 1997 Academic Press.

[发布日期] 1997-04-15