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New summation formulas for multivariate infinite series by using sampling theorems. (English) Zbl 0829.40001

The aim of this paper is to show how sampling theory can play an important role in summing up infinite series in several variables. This will be demonstrated by deriving several summation formulas for doubly infinite series that are believed to be new. One of the interesting features of this work is that although the formulas appear to be complicated, their proof are rather easy and straightforward when sampling theorems are employed. The summation formulas are derived by using theorems on both uniform and non-uniform sampling.

MSC:

40B05 Multiple sequences and series
40C15 Function-theoretic methods (including power series methods and semicontinuous methods) for summability
33E20 Other functions defined by series and integrals
94A11 Application of orthogonal and other special functions
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References:

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