A fast floating-point square-rooting routine for the 8080/8085 microprocessors
A Fast Transform for Spherical Harmonics.
A finite integral involving a confluent hypergeometric function and Meijer's G-function
A first order -difference system for the -type Jackson integral and its applications.
A function related to the central limit theorem
A number of properties of a function which originally appeared in a problem proposed by Ramanujan are presented. Several equivalent representations of the function are derived. These can be used to evaluate the function. A new derivation of an expansion in inverse powers of the argument of the function is obtained, as well as rational expressions for higher order coefficients.
A functional inequality for the survival function of the gamma distribution.
A general quadrature formula using zeros of spherical Bessel functions as nodes
We obtain, for entire functions of exponential type satisfying certain integrability conditions, a quadrature formula using the zeros of spherical Bessel functions as nodes. We deduce from this quadrature formula a result of Olivier and Rahman, which refines itself a formula of Boas.
A generalization of Bateman's expansion and finite integrals of Sonine's and Feldheim's type
Let be a sequence of arbitrary complex numbers, let α,β > -1, let Pₙα,βn=0+∞
A generalization of Gosper's algorithm to bibasic hypergeometric summation.
A generalization of Lerch’s formula
We give higher-power generalizations of the classical Lerch formula for the gamma function.
A generalization of the Bernoulli polynomials.
A generalization of the dual Beta-Function model.
A generalization of the Weber-Schafheitlin integral.
A generalized beta function and associated probability density.
A generalized inversion formula for the continuous Jacobi transform.
A geometric study of the hypergeometric function with imaginary exponents.
A geometrical proof of a new inequality for the gamma function.
A hybrid of Darboux's method and singularity analysis in combinatorial asymptotics.
A limit relation for Dunkl-Bessel functions of type A and B.
A logarithmically completely monotonic function involving the Gamma functions.