Definite integrals and operational methods

Definite Integrals using Orthogonality and Integral Transforms

We obtain definite integrals for products of associated Legendre functions with Bessel functions, associated Legendre functions, and Chebyshev polynomials of the first kind using orthogonality and integral transforms.

Solving Some Definite Integrals by Using Maple

This study uses the mathematical software Maple for the auxiliary tool to evaluate two types of definite integrals. We can obtain the closed forms of these two types of definite integrals by using differentiation with respect to a parameter and Leibniz differential rule. At the same time, we provide some definite integrals to do calculation practically. The research methods adopted in this stud...

Some Definite Integrals Involving Algebraic, Trigonometric and Bessel Functions

Some defin ite analytic integrals involving algebraic, trigonometric and Bessel functions which are needed in some electromagnetic calculations are proposed. The mathematical expansions are based on Mathematica (Wolfram) software and on some well known formulas. The agreement between the present expansion results and the numerical evaluation results is excellent.

A Lost Theorem: Definite Integrals in an Asymptotic Setting

We present a simple yet rigorous theory of integration that is based on two axioms rather than on a construction involving Riemann sums. With several examples we demonstrate how to set up integrals in applications of calculus without using Riemann sums. In our axiomatic approach even the proof of the existence of the definite integral (which does use Riemann sums) becomes slightly more elegant ...

Some Definite Integrals Associated with the Riemann Zeta Function