Some summation formulas for the series $\sb 3F\sb 2(1)$

Some Summation Formulas for the Hypergeometric

The aim of this paper is to obtain explicit expressions of the generalized hypergeometric function r+2Fr+1 [ a, b, 1 2 (a+ b+ j + 1), (fr +mr) (fr) ; 1 2 ] for j = 0,±1, . . . ,±5, where r pairs of numeratorial and denominatorial parameters differ by positive integers mr. The results are derived with the help of an expansion in terms of a finite sum of 2F1( 1 2 ) functions and a generalization ...

Some q-Dixon-like summation formulas

We give a q-analogue of some Dixon-like summation formulas obtained by Gould and Quaintance [Fibonacci Quart. 48 (2010), 56–61] and Chu [Integral Transforms Spec. Funct. 23 (2012), 251–261], respectively. For example, we prove that

Some summation formulas involving harmonic numbers and generalized harmonic numbers

Closed-form Summation of Some Trigonometric Series

The problem of numerical evaluation of the classical trigonometric series ^ sin(2fr+ l)a . ^ cOS(2/c + l)a ¿„(a) = > ——;-—— ana C„(a) = > —rr-,-t;—» £j (2k+1)" ÍTo Vk+XY where v > 1 in the case of Sin(a) and C2„+X(a) with n = 1, 2, 3, ... has been recently addressed by Dempsey, Liu, and Dempsey; Boersma and Dempsey; and by Gautschi. We show that, when a is equal to a rational multiple of 2k , t...

New Proofs of Some q-Summation and q-Transformation Formulas

We obtain an expectation formula and give the probabilistic proofs of some summation and transformation formulas of q-series based on our expectation formula. Although these formulas in themselves are not the probability results, the proofs given are based on probabilistic concepts.