This volume provides self-contained proofs of a variety of entries in the frequently used table of integrals by I.S. Gradshteyn and I.M. Ryzhik. It collects 14 papers from Revista Scientia covering elliptic integrals, the Riemann zeta function, the error function, hypergeometric and hyperbolic functions, Bessel-K functions, logarithms and rational functions, polylogarithm functions, the exponential integral, and Whittaker functions. The book gives the most elementary arguments possible and uses Mathematica ® to verify the formulas.
This volume provides self-contained proofs of a variety of entries in the frequently used table of integrals by I.S. Gradshteyn and I.M. Ryzhik. It collects 14 papers from Revista Scientia covering elliptic integrals, the Riemann zeta function, the error function, hypergeometric and hyperbolic functions, Bessel-K functions, logarithms and rational functions, polylogarithm functions, the exponential integral, and Whittaker functions. The book gives the most elementary arguments possible and uses Mathematica ® to verify the formulas.
Victor H. Moll is a professor in the Department of Mathematics at Tulane University. His research interests include special functions, number theory, and symbolic computation.
Inhaltsangabe
Complete elliptic integrals. The Riemann zeta function. Some automatic proofs. The error function. Hypergeometric functions. Hyperbolic functions. Bessel-K functions. Combination of logarithms and rational functions. Polylogarithm functions. Evaluation by series. The exponential integral. More logarithmic integrals. Confluent hypergeometric and Whittaker functions. Evaluation of entries in Gradshteyn and Ryzhik employing the method of brackets. The list of integrals. References.
Complete elliptic integrals. The Riemann zeta function. Some automatic proofs. The error function. Hypergeometric functions. Hyperbolic functions. Bessel-K functions. Combination of logarithms and rational functions. Polylogarithm functions. Evaluation by series. The exponential integral. More logarithmic integrals. Confluent hypergeometric and Whittaker functions. Evaluation of entries in Gradshteyn and Ryzhik employing the method of brackets. The list of integrals. References.
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