Browsing by Subject "Generalized hypergeometric series"
Now showing items 18 of 8

An alternative proof of the extended Saalschütz summation theorem for the r + 3Fr + 2(1) series with applications
(John Wiley & Sons, 20150306)A simple proof is given of a new summation formula recently added in the literature for a terminating r + 3Fr + 2(1) hypergeometric series for the case when r pairs of numeratorial and denominatorial parameters differ by ... 
Certain transformations and summations for generalized hypergeometric series with integral parameter differences
(Taylor & Francis, 201101)Certain transformation and summation formulas for generalized hypergeometric series with integral parameter differences are derived. 
Comments on "New hypergeometric identities arising from Gauss’s second summation theorem"
(Miskolc University Press, 2012)In 1997, Exton [J. Comput. Appl. Math. 88 (1997) 269–274] obtained a general transfor mation involving hypergeometric functions by elementary manipulation of series. A number of hypergeometric identities not previously ... 
An extension of Saalschütz's summation theorem for the series r+3Fr+2
(Taylor & Francis, 2013)The aim in this research note is to provide an extension of Saalschütz's summation theorem for the series r+3Fr+2(1) when r pairs of numeratorial and denominatorial parameters differ by positive integers. The result is ... 
A note on a hypergeometric transformation formula due to Slater with an application
(Hilaris, 2015)In this note we state (with minor corrections) and give an alternative proof of a very general hypergeometric transformation formula due to Slater. As an application, we obtain a new hypergeometric transformation formula ... 
On a new class of summation formulae involving the Laguerre polynomial
(Taylor & Francis, 2012)By elementary manipulation of series, a general transformation involving the generalized hypergeometric function is established. Kummer’s first theorem, the classical Gauss summation theorem and the generalized Kummer ... 
On two Thomaetype transformations for hypergeometric series with integral parameter differences
(Department of Mathematics, J.J. Strossmayer University of Osijek, 2014)We obtain two new Thomaetype transformations for hypergeometric series with r pairs of numeratorial and denominatorial parameters differing by positive integers. This is achieved by application of the socalled Beta ... 
Some summation formulas for the hypergeometric series r+2Fr+1(1/2)
(Hacettepe University Faculty of Science, 2013)