Per W. Karlsson

Some reduction formulae for double power series and Kampé de Fériet functions

Abstract Application of suitable 4F3[1] summation theorems leads to a number of formulae expressing certain double power series with equal variables as single power series. These formulae yield as particular cases reduction formulae expressing Kampe de Feriet functions Fq:1:1p:2:2[X,X] with certain parameter conditions in terms of either p+3Fq+2[X] or p+2Fq+1[X].

Some formulae for double Clausenian functions

Abstract For certain F q : s ; s p : r ; r [ x , y ] functions with p + r =3 and q + s =2, reduction and transformation formulae under various conditions upon variables and parameters are derived from an Euler integral representation that requires one relation between parameters.

Reduction of certain multiple hypergeometric functions

Abstract It is shown that a generalized Kampe de Feriet function whose variables are all equal and whose parameters satisfy certain relations reduces to a single hypergeometric function.

Integral representations of Euler's type for certain generalized Horn functions

Several integral representations of Eulers type for the generalized Horn functions (k)H3(n) and (k)H4(n) are given; and quadratic transformations expressing these as FD(n) and FA(n), respectively, are derived. Moreover, a reduction formula expressing (k)H3(n) in terms of (1)H3(n) is given.

Inductance and hypergeometric functions. II

Abstract Vector potential and inductances for simple current distributions with rotational symmetry are considered. The approach is in terms of those hypergeometric functions that yield the simplest expressions, rather than complete elliptic integrals. In particular, an integral for the self-inductance of a solenoid of arbitrary thickness and length is given.