These are the papers that contain the proofs of entries in

the table of integrals by Gradshteyn and Ryzhik.

If you would like a hard copy, please email me at vhm at math.tulane.edu

- The integrals in Gradshteyn and Ryzhik. Part 30: Trigonometric functions

(with T. Amdeberhan, A. Dixit, X. Guan, L. Jiu, A. Kuznetsov and C. Vignat) (28 pages).

Scientia, Series A: Math. Sciences ??, 20??, ??.

A variety of entries in the table by Gradshteyn and Ryzhik where the integrand

contains trigonometric functions are evaluated.

- The integrals in Gradshteyn and Ryzhik. Part 29: Chebyshev polynomials

(with C. Vignat) (15 pages).

Scientia, Series A: Math. Sciences ??, 20??, ??.

A variety of entries in the table by Gradshteyn and Ryzhik where the integrand

contains the Chebyshev polynomials are evaluated.

- Evaluation of entries in Gradshteyn and Ryzhik employing the method of brackets

(with I. Gonzalez and K. Kohl) (20 pages).

Scientia, Series A: Math. Sciences 25, 2014, 65-84.

The method of brackets is used ito evaluate a selection of entries in

the table by Gradshteyn and Ryzhik.

- The integrals in Gradshteyn and Ryzhik. Part 28: The confluent hypergeometric function and Whittaker functions

(with A. Dixit) (13 pages).

Scientia, Series A: Math. Sciences ??, 20??, ??.

A variety of entries in the table by Gradshteyn and Ryzhik where the integrand

contains the Whittaker function are evaluated.

- The integrals in Gradshteyn and Ryzhik. Part 27: More logarithmic examples

(with L. Medina) (17 pages).

Scientia, Series A: Math. Sciences ??, 20??, ??.

A variety of entries in the table by Gradshteyn and Ryzhik where the integrand

contains logarithms of elementary functions are evaluated.

- The integrals in Gradshteyn and Ryzhik. Part 26: The exponential integral

(with K. Boyadzhiev) (12 pages).

Scientia, Series A: Math. Sciences ??, 20??, ??.

A variety of entries in the table by Gradshteyn and Ryzhik that contain the

exponential integral are evaluated.

- The integrals in Gradshteyn and Ryzhik. Part 25: Evaluation by series

(13 pages).

Scientia, Series A: Math. Sciences 23, 2012, 53-65.

A variery of entries in the table by Gradshteyn and Ryzhik are evaluated

in terms of infinite series.

- The integrals in Gradshteyn and Ryzhik. Part 24: Polylogarithms functions

(with K. McInturff) (7 pages).

Scientia, Series A: Math. Sciences 23, 2012, 45-51.

Some entries in the table by Gradshteyn and Ryzhik are evaluated

using the polylogarithmic function.

- The integrals in Gradshteyn and Ryzhik. Part 23: Combination of logarithms and rational functions

(with L. Medina) (18 pages).

Scientia, Series A: Math. Sciences 23, 2012, 1-18.

A systematic analysis of many of the entries in the table by Gradshteyn and Ryzhik that

have an integrand that combines logarithms and rational functions is provided.

- The integrals in Gradshteyn and Ryzhik. Part 22: Bessel-K functions

(with L. Glasser, K. Kohl, C. Koutschan and A. Straub) (23 pages).

Scientia, Series A: Math. Sciences 22, 2012, 129-151.

A systematic analysis of many of the entries in the table by Gradshteyn and Ryzhik that

have an elementary integrand and the answer involves the Bessel-K function is provided.

- The integrals in Gradshteyn and Ryzhik. Part 21: Hyperbolic functions

(with K. Boyadzhiev) (19 pages).

Scientia, Series A: Math. Sciences 22, 2012, 109-127.

A systematic analysis of many of the entries in the table by Gradshteyn and Ryzhik that

involve hyperbolic functions is provided.

- The integrals in Gradshteyn and Ryzhik. Part 20: Hypergeometric functions

(with K. Kohl) (12 pages).

Scientia, Series A: Math. Sciences 21, 2011, 43-54.

The evaluation of a selection of entries from the table of integrals by

Gradshteyn and Ryzhik that involve the hypergeometric function is presented.

- The integrals in Gradshteyn and Ryzhik. Part 19: The error function

(with M. Albano, T. Amdeberhan and E. Beyerstedt) (18 pages).

Scientia, Series A: Math. Sciences 21, 2011, 25-42.

The evaluation of a selection of entries from the table of integrals by

Gradshteyn and Ryzhik that involve the error function is presented.

- The integrals in Gradshteyn and Ryzhik. Part 18: Some automatic proofs

(with C. Koutschan) (19 pages).

Scientia, Series A: Math. Sciences 20, 2011, 93-111.

The evaluation of a selection of entries from the table of integrals by

Gradshteyn and Ryzhik is presented using the symbolic package {\bf HolonomicFunctions}

- The integrals in Gradshteyn and Ryzhik. Part 17: The Riemann zeta function

(with T. Amdeberhan and K. Boyadzhiev) (11 pages).

Scientia, Series A: Math. Sciences 20, 2011, 61-71.

A systematic analysis of many of the entries in the table by Gradshteyn and Ryzhik that

involve the Riemann zeta function is provided.

- The integrals in Gradshteyn and Ryzhik. Part 16: Complete elliptic integrals

(with Stefan Boettner) (15 pages).

Scientia, Series A: Math. Sciences 20, 2011, 45-59.

A systematic analysis of many of the entries in the table by Gradshteyn and Ryzhik that

involve complete elliptic integrals is provided.

- The integrals in Gradshteyn and Ryzhik. Part 15: Frullani integrals

(with Matthew Albano, Tewodros Amdeberhan and Erin Beyerstedt) (7 pages).

Scientia, Series A: Math. Sciences 19, 2010, 113-119.

We provide evaluations of a variety of integrals that fit the Frullani type format.

One example where the integrand does not have a limit at infinity is discussed in detail.

- The integrals in Gradshteyn and Ryzhik. Part 14: An elementary evaluation of entry 3.411.5

(with Tewodros Amdeberhan) (7 pages).

Scientia, Series A: Math. Sciences 19, 2010, 97-103. (7 pages).

We provide an elementary evaluation of a series that gives entry 3.411.5 in the table of integrals

by I. M. Gradshteyn and Ryzhik. It involves a special value of the dilogarithm function.

- The integrals in Gradshteyn and Ryzhik. Part 13:
Trigonometric forms of the beta function

Scientia, Series A: Math. Sciences 19, 2010, 91-96. (6 pages).

We present the evaluation of some integrals in the table of Gradhsteyn and Ryzhik

where the integrand involves trigonometric functions and the result is expressed in terms

of the beta function.

- The integrals in Gradshteyn and Ryzhik. Part 12:
Some logarithmic integrals

(with R. Posey) (8 pages).

Scientia, Series A: Math. Sciences 18, 2009, 77-84.

We present the evaluation of some integrals in the table of Gradhsteyn and Ryzhik

where the integrand is the product of a rational function with comples poles and the logarithm function.

- The integrals in Gradshteyn and Ryzhik. Part 11:
The incomplete beta function

(with K. Boyadzhiev and L. Medina) (15 pages).

Scientia, Series A: Math. Sciences 18, 2009, 61-75.

We present the evaluation of some integrals in the table of Gradhsteyn and Ryzhik

that are involve the incomplete beta function.

- The integrals in Gradshteyn and Ryzhik. Part 10:
The digamma function

Scientia, Series A: Math. Sciences 17, 2009, 45-66.

(with L. Medina) (22 pages).

We present the evaluation of some integrals in the table of Gradhsteyn and Ryzhik

that are involve the digamma function ( the logarithmic derivative of the gamma function).

- The integrals in Gradshteyn and Ryzhik. Part 9:
Combinations of logarithms, rational and trigonometric functions

(with T. Amdeberhan, J. Rosenberg, A. Straub and P. Whitworth) (18 pages).

Scientia, Series A: Math. Sciences 17, 2009, 27-44.

We present the evaluation of some integrals in the table of Gradhsteyn and Ryzhik

that are combinations of logarithms and rational functions. Some trigonometric

versions of the integrals are also presented.

- The integrals in Gradshteyn and Ryzhik. Part 8:
Combinations of powers, exponentials and logarithms

(with A. Straub, J. Rosenberg and P. Whitworth) (10 pages).

Scientia, Series A: Math. Sciences 16, 2008, 41-50.

We present the evaluation of some integrals in the table of Gradhsteyn and Ryzhik

that are combinations of powers, exponentials and logarithms.

- The integrals in Gradshteyn and Ryzhik. Part 7:
Elementary examples
(with T. Amdeberhan) (14 pages).

Scientia, Series A: Math. Sciences 16, 2008, 25-40.

We present some elementary integrals that appear in the table of Gradhsteyn and Ryzhik.

- The integrals in Gradshteyn and Ryzhik. Part 6:
The beta function
(14 pages).

Scientia, Series A: Math. Sciences 16, 2008, 9-24.

We present some elementary integrals that can be expressed in terms of the beta function.

- The integrals in Gradshteyn and Ryzhik. Part 5:
Some trigonometric integrals
(with T. Amdeberhan and L. Medina).

Scientia, Series A: Math. Sciences 15, 2007, 47-60.

We present the evaluations of definite integrals involving x^p times integer powers of cos x.

- The integrals in Gradshteyn and Ryzhik. Part 4:
The gamma function

Scientia, Series A: Math. Sciences 15, 2007, 37-46.

We present some elementary integrals that can be expressed in terms of the gamma function.

- The integrals in Gradshteyn and Ryzhik. Part 3: Combinations of
logarithms and exponentials

Scientia, Series A: Math. Sciences 15, 2007, 31-36.

We present some elementary integrals that are combinations of logarithms and exponentials.

- The integrals in Gradshteyn and Ryzhik. Part 2: elementary logarithmic integrals

Scientia, Series A: Math. Sciences 14, 2007, 7-15.

We present the evaluation of elementary integrals of the form

R(x) times log(x). The results involve the dilogarithm function.

- The integrals in Gradshteyn and Ryzhik. Part 1: a family of logarithmic integrals

Scientia, Series A: Math. Sciences 14, 2007, 1-6.

We present the evaluation of a family of integrals of the form: power of log x times

a rational function with two poles.

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