Results 1 
3 of
3
Handtohand combat with thousanddigit integrals
, 2010
"... In this paper we describe numerical investigations of definite integrals that arise by considering the moments of multistep uniform random walks in the plane, together with a closely related class of integrals involving the elliptic functions K, K ′ , E and E ′. We find that in many cases such inte ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
In this paper we describe numerical investigations of definite integrals that arise by considering the moments of multistep uniform random walks in the plane, together with a closely related class of integrals involving the elliptic functions K, K ′ , E and E ′. We find that in many cases such integrals can be “experimentally ” evaluated in closed form or that intriguing linear relations exist within a class of similar integrals. Discovering these identities and relations often requires the evaluation of integrals to extreme precision, combined with largescale runs of the “PSLQ ” integer relation algorithm. This paper presents details of the techniques used in these calculations and mentions some of the many difficulties that can arise.
Crandall’s computation of the incomplete Gamma Function and the Hurwitz Zeta Function with applications to Dirichlet Lseries
, 2014
"... This paper extends tools developed by Richard Crandall in [16] to provide robust, highprecision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to the corresponding computation of the Hurwitz zeta function and so of Dirichlet Lseries and cha ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
This paper extends tools developed by Richard Crandall in [16] to provide robust, highprecision methods for computation of the incomplete Gamma function and the Lerch transcendent. We then apply these to the corresponding computation of the Hurwitz zeta function and so of Dirichlet Lseries and character polylogarithms.
Remarks on Slater’s Asymptotic Expansions of Kummer Functions for Large Values of the aParameter
"... To the memory of Panayiotis D. Siafarikas. The man who loved special functions. In Slater’s 1960 standard work on confluent hypergeometric functions, also called Kummer functions, a number of asymptotic expansions of these functions can be found. We summarize expansions derived from a differential e ..."
Abstract
 Add to MetaCart
(Show Context)
To the memory of Panayiotis D. Siafarikas. The man who loved special functions. In Slater’s 1960 standard work on confluent hypergeometric functions, also called Kummer functions, a number of asymptotic expansions of these functions can be found. We summarize expansions derived from a differential equation for large values of the aparameter. We show how similar expansions can be derived by using integral representations, and we observe discrepancies with Slater’s expansions.