## 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…