Some evaluations for the generalized hypergeometric series

Summation theorems for multidimensional basic hypergeometric series by determinant evaluations

Extension of Some Classical Summation Theorems for the Generalized Hypergeometric Series with Integral Parameter Differences

We derive extensions of the classical summation theorems of Kummer and Watson for the generalized hypergeometric series where r pairs of numeratorial and denominatorial parameters differ by positive integers. The results are obtained with the help of a generalization of Kummer’s second summation theorem for the 2F1 series given recently by Rakha and Rathie [Integral Transforms and Special Funct...

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...

Some Properties of Generalized Hypergeometric Thermal Coherent States

Abstract: The generalized hypergeometric coherent states (GHCSs) have been introduced by Appl and Schiller [1]. In the present paper we have extended some considerations about GHCSs to the mixed (thermal) states and applied, particularly, to the case of pseudoharmonic oscillator (PHO). The Husimi’s Q distribution function and the diagonal P distribution function, in the GHCSs representation, ha...

Summations and Transformations for Multiple Basic and Elliptic Hypergeometric Series by Determinant Evaluations

Abstract. Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey’s nonterminating 10φ9 transformation. From this result, we deduce new multivariable terminating 10φ9 transformations, 8φ7 summations and other identities. We also use similar methods to derive new multivariable 1ψ1 and 6ψ6 summations. Some of our results are extended to the case o...