Generalized Summation Formulas for the KampÉ de FÉriet Function

0 N ov 1 99 5 Transformation and summation formulas for Kampé

The double hypergeometric Kampé de Fériet series F 0:3 1:1 (1, 1) depends upon 9 complex parameters. We present three cases with 2 relations between those 9 parameters, and show that under these circumstances F 0:3 1:1 (1, 1) can be written as a 4 F 3 (1) series. Some limiting cases of these transformation formulas give rise to new summation results for special F 0:3 1:1 (1, 1)'s. The actual tr...

Generalized Poisson Summation Formulas for Continuous Functions of Polynomial Growth

The Poisson summation formula (PSF) describes the equivalence between the sampling of an analog signal and the periodization of its frequency spectrum. In engineering textbooks, the PSF is usually stated formally without explicit conditions on the signal for the formula to hold. By contrast, in themathematics literature, the PSF is commonly stated and proven in the pointwise sense for various t...

Some summation formulas involving harmonic numbers and generalized harmonic numbers

Recursive Formulas Related to the Summation of the Möbius Function

For positive integers n, let μ(n) be the Möbius function, and M(n) its sum M(n) = Pn k=1 μ(k). We find some identities and recursive formulas for computing M(n); in particular, we present a two-parametric family of recursive formulas.

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 ...