## 6,412 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…

### A Short Note on Integral Transformations and Conversion Formulas for Sequence Generating Functions

- MathematicsAxioms
- 2019

Two variants of the OGF-to-EGF transformation integrals from the Hankel loop contour for the reciprocal gamma function and from Fourier series expansions of integral representations for the Hadamard product of two generating functions, respectively are proved.

### 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 Functions

- Mathematics2015 IEEE 22nd Symposium on Computer Arithmetic
- 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…

### 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…

### In Quest of Bernstein Inequalities Rational Functions, Askey-Wilson Operator, and Summation Identities for Entire Functions

- Mathematics
- 2018

The title of the dissertation gives an indication of the material involved with the connecting thread throughout being the classical Bernstein inequality (and its variants), which provides an…

### Fourier interpolation from spheres

- MathematicsTransactions of the American Mathematical Society
- 2020

In every dimension $d \geq 5$ we give an explicit formula that expresses the values of any Schwartz function on $\mathbb{R}^d$ only in terms of its restrictions, and the restrictions of its Fourier…