Zayed, Ahmed I. New summation formulas for multivariate infinite series by using sampling theorems. (English) Zbl 0829.40001 Appl. Anal. 54, No. 1-2, 135-150 (1994). 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. Reviewer: A.I.Zayed (Orlando) Cited in 1 Document 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 Keywords:sampling series; multivariate infinite series; special functions; summation formulas PDFBibTeX XMLCite \textit{A. I. Zayed}, Appl. Anal. 54, No. 1--2, 135--150 (1994; Zbl 0829.40001) Full Text: DOI References: [1] Butzer P., J. Math. Res. Exposition 3 pp 185– (1983) [2] Erdelyi A., Tables of Integral Transforms · Zbl 0456.47025 [3] Gradshteyn I., Tables o Integrals, Series and Products · Zbl 0918.65002 [4] DOI: 10.1090/S0273-0979-1985-15293-0 · Zbl 0562.42002 · doi:10.1090/S0273-0979-1985-15293-0 [5] DOI: 10.1109/PROC.1977.10771 · Zbl 0442.94002 · doi:10.1109/PROC.1977.10771 [6] Zayed A., Journal of Math. 51 pp 575– (1991) [7] DOI: 10.1137/0150053 · Zbl 0695.41002 · doi:10.1137/0150053 [8] DOI: 10.1080/00036818808839723 · Zbl 0611.94001 · doi:10.1080/00036818808839723 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.