Symmetric inclusion-exclusion.
Theorems on the Convergence of Series in Generalized Lommel-Wright Functions
Mathematics Subject Classification: 30B10, 30B30; 33C10, 33C20The classical Cauchy-Hadamard, Abel and Tauber theorems provide useful information on the convergence of the power series in complex plane. In this paper we prove analogous theorems for series in the generalized Lommel-Wright functions with 4 indices. Results for interesting special cases of series involving Bessel, Bessel-Maitland, Lommel and Struve functions, are derived.We provide also a new asymptotic formula for the generalized ...
Transformation formulas for terminating Saalschützian hypergeometric series of unit argument.
Ueber die Functionen, welche durch Reihen von der Form dargestellt werden ... .
Uniformly starlike functions and uniformly convex functions related to the Pascal distribution
In this article, we aim to find sufficient conditions for a convolution of analytic univalent functions and the Pascal distribution series to belong to the families of uniformly starlike functions and uniformly convex functions in the open unit disk . We also state corollaries of our main results.
Well-poised hypergeometric service for diophantine problems of zeta values
It is explained how the classical concept of well-poised hypergeometric series and integrals becomes crucial in studying arithmetic properties of the values of Riemann’s zeta function. By these well-poised means we obtain: (1) a permutation group for linear forms in and yielding a conditional upper bound for the irrationality measure of ; (2) a second-order Apéry-like recursion for and some low-order recursions for linear forms in odd zeta values; (3) a rich permutation group for a family...