@inproceedings{6aa71aeadac9498ca6bb4d74183e1c3b,

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

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.",

keywords = "Double exponential formula, Gamma function, Verified bound",

author = "Naoya Yamanaka and Tomoaki Okayama and Shin{\textquoteright}ichi Oishi",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing Switzerland 2016.; 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015 ; Conference date: 11-11-2015 Through 13-11-2015",

year = "2016",

doi = "10.1007/978-3-319-32859-1_19",

language = "English",

isbn = "9783319328584",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "224--228",

editor = "Kotsireas, {Ilias S.} and Rump, {Siegfried M.} and Yap, {Chee K.}",

booktitle = "Mathematical Aspects of Computer and Information Sciences - 6th International Conference, MACIS 2015, Revised Selected Papers",

}