Special integrals of Gradshetyn and Ryzhik. The proofs. Volume II (2015)

• Record Type: Book
• Further Information: Note: Victor H. Moll.
• Authors: Moll, Victor H, 1956-
• Contents: Complete elliptic integrals; Introduction; Some examples; An elementary transformation; Some principal value integrals; The hypergeometric connection; Evaluation by series expansions; A small correction to a formula in Gradshteyn and Ryzhik The Riemann zeta function ; Introduction; A first integral representation; Integrals involving partial sums of ζ(s); The alternate version; The logarithmic scale; The alternating logarithmic scale; Integrals over the whole line Some automatic proofs ; Introduction; The class of holonomic functions; A first example: The indefinite form of Wallis’ integral; A differential equation for hypergeometric functions in two variables; An integral involving Chebyshev polynomials; An integral involving a hypergeometric function; An integral involving Gegenbauer polynomials; The product of two Bessel functions; An example involving parabolic cylinder functions; An elementary trigonometric integral The error function ; Introduction; Elementary integrals; Elementary scaling; A series representation for the error function; An integral of Laplace; Some elementary changes of variables; Some more challenging elementary integrals; Differentiation with respect to a parameter; A family of Laplace transforms; A family involving the complementary error function; A final collection of examples Hypergeometric functions ; Introduction; Integrals over [0, 1]; A linear scaling; Powers of linear factors; Some quadratic factors; A single factor of higher degree; Integrals over a half-line; An exponential scale; A more challenging example; One last example: A combination of algebraic factors and exponentials Hyperbolic functions ; Introduction; Some elementary examples; An example that is evaluated in terms of the Hurwitz zeta function; A direct series expansion; An example involving Catalan’s constant; Quotients of hyperbolic functions; An evaluation by residues; An evaluation via differential equations; Squares in denominators; Two integrals giving beta function values; The last two entries of Section 3.525 Bessel-K functions; Introduction; A first integral representation of modified Bessel functions; A second integral representation of modified Bessel functions; A family with typos; The Mellin transform method; A family of integrals and a recurrence; A hyperexponential example Combination of logarithms and rational functions; Introduction; Combinations of logarithms and linear rational functions; Combinations of logarithms and rational functions with denominators that are squares of linear terms; Combinations of logarithms and rational functions with quadratic denominators; An example via recurrences; An elementary example; Some parametric examples; Integrals yielding partial sums of the zeta function; A singular integral Polylogarithm functions ; Introduction; Some examples from the table by Gradshteyn and Ryzhik Evaluation by series; Introduction; A hypergeometric example; An integral involving the binomial theorem; A product of logarithms; Some integrals involving the exponential function; Some combinations of powers and algebraic functions; Some examples related to geometric series The exponential integral; Introduction; Some simple changes of variables; Entries obtained by differentiation; Entries with quadratic denominators; Some higher degree denominators; Entries involving absolute values; Some integrals involving the logarithm function; The exponential scale More logarithmic integrals ; Introduction; Some examples involving rational functions; An entry involving the Poisson kernel for the disk; Some rational integrands with a pole at x = 1; Some singular integrals; Combinations of logarithms and algebraic functions; An example producing a trigonometric answer Confluent hypergeometric and Whittaker functions; Introduction; A sample of formulas Evaluation of entries in Gradshteyn and Ryzhik employing the method of brackets; Introduction; The method of brackets; Examples of index 0; Examples of index 1 ; Examples of index 2; The goal is to minimize the index; The evaluation of a Mellin transform; The introduction of a parameter The list of integrals; The list References
• Edition: 1st
• Publisher Details: Boca Raton : Chapman & Hall/CRC
• Publication Date: 2015
• Extent: 1 online resource
• Subjects: 515.43; Definite integrals; Integrals, Logarithmic
• Languages: English
• ISBNs: 9781482256543
• Related ISBNs: 9781482256536
• Notes: Note: Includes bibliographical references and index.; Note: Description based on CIP data; item not viewed.
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.