Some expansions of hypergeometric functions in series of hypergeometric functions

Integral Properties of Zonal Spherical Functions, Hypergeometric Functions and Invariant

Some integral properties of zonal spherical functions, hypergeometric functions and invariant polynomials are studied for real normed division algebras.

A Subclass of Analytic Functions Associated with Hypergeometric Functions

In the present paper, we have established sufficient conditions for Gaus-sian hypergeometric functions to be in certain subclass of analytic univalent functions in the unit disc $mathcal{U}$. Furthermore, we investigate several mapping properties of Hohlov linear operator for this subclass and also examined an integral operator acting on hypergeometric functions.

Polynomial series expansions for confluent and Gaussian hypergeometric functions

Based on the Hadamard product of power series, polynomial series expansions for confluent hypergeometric functions M(a, c; ·) and for Gaussian hypergeometric functions F (a, b; c; ·) are introduced and studied. It turns out that the partial sums provide an interesting alternative for the numerical evaluation of the functions M(a, c; ·) and F (a, b; c; ·), in particular, if the parameters are al...

Closed-form sums for some perturbation series involving hypergeometric functions

Infinite series of the type ∞ ∑ n=1 ( 2 )n n 1 n! 2F1(−n, b; γ; y) are investigated. Closed-form sums are obtained for α a positive integer α = 1, 2, 3, . . . . The limiting case of b → ∞, after y is replaced with x2/b, leads to ∞ ∑ n=1 ( 2 )n n 1 n! 1F1(−n, γ, x2). This type of series appears in the first-order perturbation correction for the wavefunction of the generalized spiked harmonic osc...

Hypergeometric Functions