Asymptotics and Mellin-Barnes integrals [E-Book] / R.B. Paris, D. Kaminski.
Paris, R. B., (author)
Kaminski, D., (author)
Cambridge : Cambridge University Press, 2001
1 online resource (xvi, 422 pages)
englisch
9780521790017
9780511546662
Encyclopedia of mathematics and its applications ; volume 85
Full Text
Table of Contents:
  • Order Relations
  • Asymptotic Expansions
  • Other Expansions
  • Biographies of Mellin and Barnes
  • Fundamental Results
  • The Gamma Function [Gamma] (z)
  • The Asymptotic Expansion of [Gamma] (z)
  • The Stirling Coefficients
  • Bounds for [Gamma] (z)
  • Expansion of Quotients of Gamma Functions
  • Inverse Factorial Expansions
  • A Recursion Formula when [alpha subscript r] = [beta subscript r]
  • An Algebraic Method for the Determination of the A[subscript j]
  • Special Cases
  • The Asymptotic Expansion of Integral Functions
  • Convergence of Mellin-Barnes Integrals
  • Order Estimates for Remainder Integrals
  • Lemmas
  • Properties of Mellin Transforms
  • Basic Properties
  • Translational and Differential Properties
  • The Parseval Formula
  • Analytic Properties
  • Inverse Mellin Transforms
  • Integrals Connected with e[superscript -z]
  • Some Standard Integrals
  • Discontinuous Integrals
  • Gamma-Function Integrals
  • Ramanujan-Type Integrals
  • Barnes' Lemmas
  • Mellin-Barnes Integral Representations
  • The Confluent Hypergeometric Functions
  • The Gauss Hypergeometric Function
  • Some Special Functions
  • Applications of Mellin Transforms
  • Transformation of Series
  • The Mellin Transform Method
  • The Poisson-Jacobi Formula
  • An Infinite Series
  • A Smoothed Dirichlet Series
  • A Finite Sum
  • Number-Theoretic Examples
  • A Harmonic Sum
  • Euler's Product
  • Ramanujan's Function
  • Some Other Number-Theoretic Sums
  • Solution of Differential Equations
  • Potential Problems in Wedge-Shaped Regions.