Verified error bounds for the real gamma function using double exponential formula over semi-infinite interval

Naoya Yamanaka, Tomoaki Okayama, Shin’ichi Oishi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

An algorithm is presented for computing verified error bounds for the value of the real gamma function. It has been shown that the double exponential formula is one of the most efficient methods for calculating integrals of the form. Recently, an useful evaluation based on the double exponential formula over the semi-infinite interval has been proposed. However, the evaluation would be overflow when applied to the real gamma function directly. In this paper, we present a theorem so as to overcome the problem in such a case. Numerical results are presented for illustrating effectiveness of the proposed theorem in terms of the accuracy of the calculation.

Original languageEnglish
Title of host publicationMathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers
EditorsIlias S. Kotsireas, Siegfried M. Rump, Chee K. Yap
PublisherSpringer Verlag
Pages224-228
Number of pages5
ISBN (Print)9783319328584
DOIs
Publication statusPublished - 2016
Event6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015 - Berlin, Germany
Duration: 2015 Nov 112015 Nov 13

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9582
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Other

Other6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015
CountryGermany
CityBerlin
Period15/11/1115/11/13

Keywords

  • Double exponential formula
  • Gamma function
  • Verified bound

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)

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