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A Distributional Representation of Gamma Function with Generalized Complex Domian
Department of Mathematics, Government College University, Faisalabad, Pakistan
Department of Mathematics, Government College University, Faisalabad, Pakistan
Department of Mathematics, Government College University, Faisalabad, Pakistan
- 1 Department of Mathematics, Government College University, Faisalabad, Pakistan
- 2 Department of Mathematics, Government College University, Faisalabad, Pakistan
- 3 Department of Mathematics, Government College University, Faisalabad, Pakistan
Advances in Pure Mathematics·Volume 07 (2017)·Pages 441–449·Published 28 July 2017·DOI10.4236/apm.2017.78029
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Abstract
In this paper, we present a new representation of gamma function as a series of complex delta functions. We establish the convergence of this representation in the sense of distributions. It turns out that the gamma function can be defined over a space of complex test functions of slow growth denoted by Z. Some properties of gamma function are discussed by using the properties of delta function.
KeywordsGamma FunctionDistributions or Generalized FunctionsFourier TransformDirac Delta FunctionSpace of Complex Test Functions
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