Relativistic Coulomb Integrals and Zeilberger’s Holonomic Systems Approach. I

DOI10.1007/978-3-7091-1616-6_9zbMath1308.81084arXiv1206.2071OpenAlexW1662239377MaRDI QIDQ5244923

Paule, Peter, Sergei K. Suslov

Publication date: 1 April 2015

Published in: Texts & Monographs in Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.2071

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Exact enumeration problems, generating functions (05A15) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10) Nonselfadjoint operator theory in quantum theory including creation and destruction operators (81Q12)

Related Items (3)

An Introduction to Special Functions with Some Applications to Quantum Mechanics ⋮ The moments of the hydrogen atom by the method of brackets ⋮ Creative Telescoping for Holonomic Functions

Cites Work

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• The concrete tetrahedron. Symbolic sums, recurrence equations, generating functions, asymptotic estimates
• Parameterized telescoping proves algebraic independence of sums
• A fast algorithm for proving terminating hypergeometric identities
• A holonomic systems approach to special functions identities
• The method of creative telescoping
• Symbolic summation assists combinatorics
• Some Applications of Hypervirial Theorems to the Calculation of Average Values
• The Hahn polynomials in the nonrelativistic and relativistic Coulomb problems
• Summation in Finite Terms
• Decision procedure for indefinite hypergeometric summation
• Advanced applications of the holonomic systems approach
• Two-time Green's function method in quantum electrodynamics of high-\(Z\) few-electron atoms

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