6,561 Citations
INTEGRALS OF FUNCTIONS CONTAINING PARAMETERS 1 Integrals of functions containing parameters
- Mathematics
- 2020
Calculus students are taught that an indefinite integral is defined only up to an additive constant, and as a consequence generations of students have assiduously added “ +C ” to their calculus…
Indefinite integrals of products of special functions
- Mathematics
- 2017
ABSTRACT A method is given for deriving indefinite integrals involving squares and other products of functions which are solutions of second-order linear differential equations. Several variations of…
An exact integral-to-sum relation for products of Bessel functions
- MathematicsProceedings of the Royal Society A
- 2021
A useful identity relating the infinite sum of two Bessel functions to their infinite integral was discovered in Dominici et al. (Dominici et al. 2012 Proc. R. Soc. A 468, 2667–2681). Here, we extend…
Indefinite Integrals of Spherical Bessel Functions
- Mathematics
- 2017
Highly oscillatory integrals, such as those involving Bessel functions, are best evaluated analytically as much as possible, as numerical errors can be difficult to control. We investigate indefinite…
Precise and Fast Computation of Elliptic Integrals and Elliptic Functions
- Mathematics
- 2015
Summarized is the recent progress of the new methods to compute Legendre’s complete and incomplete elliptic integrals of all three kinds and Jacobian elliptic functions. Also reviewed are the…
Euler Sums and Integral Connections
- MathematicsMathematics
- 2019
In this paper, we present some Euler-like sums involving partial sums of the harmonic and odd harmonic series. First, we give a brief historical account of Euler’s work on the subject followed by…
Double Integral of Logarithm and Exponential Function Expressed in terms of the Lerch Function
- MathematicsEuropean Journal of Pure and Applied Mathematics
- 2021
This paper contains new explicit computations of some integrals containing elementary functions, such as powers, logarithms, exponentials. In this work the authors use their contour integral method…
Relations between values of arithmetic Gevrey series, and applications to values of the Gamma function
- Mathematics
- 2023
We investigate the relations between the rings E , G and D of values taken at algebraic points by arithmetic Gevrey series of order either − 1 ( E -functions), 0 (analytic continuations of G…
Non-random behavior in sums of modular symbols
- MathematicsInternational Journal of Number Theory
- 2021
We give explicit expressions for the Fourier coefficients of Eisenstein series twisted by Dirichlet characters and modular symbols on [Formula: see text] in the case where [Formula: see text] is…
Logarithmic Integrals: A Review from Gradshteyn and Ryzhik to Recent Times
- Mathematics
- 2020
The need to evaluate Logarithmic integrals is ubiquitous in essentially all quantitative areas including mathematical sciences, physical sciences. Some recent developments in Physics namely Feynman…