Fourier transform and distributional representation of the generalized gamma function with some applications |
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Authors: | Asifa Tassaddiq Asghar Qadir |
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Institution: | Center for Advanced Mathematics and Physics, National University of Sciences and Technology, H-12 Islamabad, Pakistan |
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Abstract: | We present a Fourier transform representation of the generalized gamma functions, which leads to a distributional representation for them as a series of Dirac-delta functions. Applications of these representations are shown in evaluation of the integrals of products of the generalized gamma function with other functions. The results for Euler’s gamma function are deduced as special cases. The relation of the generalized gamma function with the Macdonald function is exploited to deduce new identities for it. |
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Keywords: | Fourier transform Parseval&rsquo s identity Gamma function Generalized gamma function Distributional representation |
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