Some Summation Theorems for Truncated Clausen Series and Applications

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...

Summation theorems for multidimensional basic hypergeometric series by determinant evaluations

Some Stability Theorems for Nonharmonic Fourier Series

The theory of nonharmonic Fourier series in L2(-ir,tr) is concerned with the completeness and expansion properties of sets of complex exponentials {e'x"'}. It is well known, for example, that the completeness of the set {e'x"'} ensures that of {e'^"'} whenever 2 lA„ ~~ M»l < oo. In this note we establish two results which guarantees that if {elX"'} is a Schauder basis for l}(—n, it), then [e'^"...

Some Liouville theorems and applications

We give exposition of a Liouville theorem established in [6] which is a novel extension of the classical Liouville theorem for harmonic functions. To illustrate some ideas of the proof of the Liouville theorem, we present a new proof of the classical Liouville theorem for harmonic functions. Applications of the Liouville theorem, as well as that of earlier ones in [5], can be found in [6, 7] an...

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...