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  • P-ISSN1226-0657
  • E-ISSN2287-6081
  • KCI

ISSN : 1226-0657

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Vol.19 No.2

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SERIES EXPANSIONS OF THE ANALYTIC FEYNMAN INTEGRAL FOR THE FOURIER-TYPE FUNCTIONAL

Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics / Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, (P)1226-0657; (E)2287-6081
2012, v.19 no.2, pp.87-102
https://doi.org/10.7468/jksmeb.2012.19.2.87
Lee, Il-Yong
Chung, Hyun-Soo
Chang, Seung-Jun
Lee,, I. , Chung,, H. , & Chang,, S. (2012). SERIES EXPANSIONS OF THE ANALYTIC FEYNMAN INTEGRAL FOR THE FOURIER-TYPE FUNCTIONAL. Journal of the Korean Society of Mathematical Education Series B: The Pure and Applied Mathematics, 19(2), 87-102, https://doi.org/10.7468/jksmeb.2012.19.2.87

Abstract

In this paper, we consider the Fourier-type functionals introduced in [16]. We then establish the analytic Feynman integral for the Fourier-type functionals. Further, we get a series expansion of the analytic Feynman integral for the Fourier-type functional <TEX>$[{\Delta}^kF]^{\^}$</TEX>. We conclude by applying our series expansion to several interesting functionals.

keywords
analytic Feynman integral, Fourier transform, Fourier-type functional, hypergeometric function, Wiener space

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