Some fractional-calculus results for the \(\overline H\)-function associated with a class of Feynman integrals

DOI10.1134/S1061920806010092zbMath1223.33027OpenAlexW1964441466MaRDI QIDQ871758

Shy-Der Lin, Pin-Yu Wang, Hari M. Srivastava

Publication date: 26 March 2007

Published in: Russian Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s1061920806010092

Mathematics Subject Classification ID

Fractional derivatives and integrals (26A33) Other hypergeometric functions and integrals in several variables (33C70) Feynman integrals and graphs; applications of algebraic topology and algebraic geometry (81Q30)

Related Items (17)

Fractional calculus of generalized \(k\)-Mittag-Leffler function and its applications to statistical distribution ⋮ Some families of the incomplete \(H\)-functions and the incomplete \(\overline H \)-functions and associated integral transforms and operators of fractional calculus with applications ⋮ Fractional integrals and solution of fractional kinetic equations involving \(k\)-Mittag-Leffler function ⋮ New Chebyshev type inequalities via a general family of fractional integral operators with a modified Mittag-Leffler kernel ⋮ On fractional integration formulae for Aleph functions ⋮ Marichev-Saigo-Maeda fractional integration operators involving generalized Bessel functions ⋮ Explicit solutions of Jacobi and Gauss differential equations by means of operators of fractional calculus ⋮ Composition formulas of Bessel-Atruve kernel function ⋮ Unnamed Item ⋮ Integral and computational representations of the extended Hurwitz–Lerch zeta function ⋮ Some families of series identities and associated fractional differintegral formulas ⋮ Explicit solutions of a certain class of differential equations by means of fractional calculus ⋮ Unnamed Item ⋮ Unnamed Item ⋮ New extension of fractional-calculus results associated with product of certain special functions ⋮ A general fractional differential equation associated with an integral operator with the \(H\)-function in the kernel ⋮ Certain Feynman type integrals involving generalized k-Mittag-Leffler function and general class of polynomials

Cites Work

• Some fractional differintegral equations
• Fractional differential equations. An introduction to fractional derivatives, fractional differential equations, to methods of their solution and some of their applications
• The Fox-Wright functions and Laguerre multiplier sequences
• The G and H Functions as Symmetrical Fourier Kernels
• The H function associated with a certain class of Feynman integrals
• New properties of hypergeometric series derivable from Feynman integrals. I. Transformation and reduction formulae
• New properties of hypergeometric series derivable from Feynman integrals II. A generalisation of the H function
• All the special functions are fractional differintegrals of elementary functions
• The Asymptotic Expansion of the Generalized Hypergeometric Function
• The Asymptotic Expansion of the Generalized Hypergeometric Function
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