In this paper, the Euler-Maclaurin formula is exploited to provide an expression for the q-factorial function as an infinite integral.
The Dirichlet test for convergence of infinite integral shows that
Since the infinite integral in the previous theorem is convergent, then we have
The real Hankel transform H[Nu]([Xi], f(x)) of a real function y = f(x) requires the evaluation of the infinite integral
The approximation for the Bessel function Piessens used allowed him to write the infinite integral as the sum of an integral over a finite interval and of a Fourier-sine and Fourier-cosine transform.
The matrix elements are given in the form of an infinite integrals.
2] ([alpha], [beta]), and K ([alpha], [beta]) and these infinite integrals are transformed into infinite series and these series are convenient for numerical computation.
The evaluation of these infinite integrals when all the terms are written out in full form become very unwidely and moreover we have to perform the inverse Laplace transform to these expressions in order to find the temperature and stresses in space time domain.
Simultaneous calculations for the inversion of double Fourier transforms were done by evaluating the infinite integrals (2.
However, the essence of his material is virtually timeless, covering real variables, functions of real variables, complex numbers, limits of functions for a positive integer variable, limits of functions of a continuous variable, derivatives and integrals, theorems in the differential and integral calculus, the convergence of infinite series and infinite integrals
, the functions of real variables (logarithmic, exponential and circular) and their real functions.
m)] method for accelerating convergence of sequences as applied to infinite integrals.
An extension of the Levin-Sidi class of nonlinear transformations for accelerating convergence of Infinite Integrals and Series.