Ramanujan's master theorem

DOI10.1007/s11139-011-9333-yzbMath1258.33001OpenAlexW2024654356WikidataQ56854461 ScholiaQ56854461MaRDI QIDQ1927667

Armin Straub, Marshall Harrison, Victor H. Moll, Ivan Gonzalez, Olivier Espinosa, Tewodoros Amdeberhane

Publication date: 2 January 2013

Published in: The Ramanujan Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11139-011-9333-y

zbMATH Keywords

integralshypergeometric functionsanalytic continuationseries representationmethod of bracketsrandom walk integrals

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Gamma, beta and polygamma functions (33B15) Classical hypergeometric functions, ({}_2F_1) (33C05)

Related Items (33)

From integrals to multi-sum identities ⋮ The spherical Bessel and Struve functions and operational methods ⋮ Exact expansions of Hankel transforms and related integrals ⋮ Dispersive effects in a scalar nonlocal wave equation inspired by peridynamics ⋮ Some results on the extended beta and extended hypergeometric functions ⋮ Ramanujan's integral identities of the Riemann \(\Xi\)-function and the Lerch transcendent ⋮ Three-Step and Four-Step Random Walk Integrals ⋮ The umbral operator and the integration involving generalized Bessel-type functions ⋮ Pochhammer symbol with negative indices. A new rule for the method of brackets ⋮ Bessel SPDEs and renormalised local times ⋮ An extension of the method of brackets. Part 1 ⋮ The Ramanujan master theorem and its implications for special functions ⋮ Integrability of conformal blocks. I: Calogero-Sutherland scattering theory ⋮ Compatibility of the method of brackets with classical integration rules ⋮ Celestial insights into the S-matrix bootstrap ⋮ Korenblum constants for various weighted Fock spaces ⋮ Laurent expansion of harmonic zeta functions ⋮ An operational calculus generalization of Ramanujan's master theorem ⋮ A connection between power series and Dirichlet series ⋮ Unnamed Item ⋮ Some new results related to a class of generalized Hurwitz zeta function ⋮ Ramanujan's master theorem applied to the evaluation of Feynman diagrams ⋮ A Fundamental Criteria to Establish General Formulas of Integrals ⋮ The moments of the hydrogen atom by the method of brackets ⋮ Symbolic methods for the evaluation of sum rules of Bessel functions ⋮ Integrals of Frullani type and the method of brackets ⋮ Definite integrals and operational methods ⋮ Formulas of absolute moments ⋮ Operational versus umbral methods and the Borel transform ⋮ On certain results related to the hypergeometric function \(F_K\) ⋮ An extension of the method of brackets. Part 2 ⋮ Ramanujan's master theorem for Sturm Liouville operator ⋮ Ramanujan's master theorem and two formulas for the zero-order Hankel transform

Cites Work

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• Some arithmetic properties of short random walk integrals
• Optimized negative dimensional integration method (NDIM) and multiloop Feynman diagram calculation
• A formula for a quartic integral: a survey of old proofs and some new ones
• On Some Families of Integrals Solvable in Terms of Polygamma and Negapolygamma Functions
• Three-Step and Four-Step Random Walk Integrals
• The double square root, Jacobi polynomials and Ramanujan's master theorem

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