### 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 language | English |
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Title of host publication | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |

Publisher | Springer Verlag |

Pages | 224-228 |

Number of pages | 5 |

Volume | 9582 |

ISBN (Print) | 9783319328584 |

DOIs | |

Publication status | Published - 2016 |

Event | 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015 - Berlin, Germany Duration: 2015 Nov 11 → 2015 Nov 13 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 9582 |

ISSN (Print) | 03029743 |

ISSN (Electronic) | 16113349 |

### Other

Other | 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015 |
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Country | Germany |

City | Berlin |

Period | 15/11/11 → 15/11/13 |

### Fingerprint

### Keywords

- Double exponential formula
- Gamma function
- Verified bound

### ASJC Scopus subject areas

- Computer Science(all)
- Theoretical Computer Science

### Cite this

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)*(Vol. 9582, pp. 224-228). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9582). Springer Verlag. https://doi.org/10.1007/978-3-319-32859-1_19

**Verified error bounds for the real gamma function using double exponential formula over semi-infinite interval.** / Yamanaka, Naoya; Okayama, Tomoaki; Oishi, Shinichi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics).*vol. 9582, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 9582, Springer Verlag, pp. 224-228, 6th International Conference on Mathematical Aspects of Computer and Information Sciences, MACIS 2015, Berlin, Germany, 15/11/11. https://doi.org/10.1007/978-3-319-32859-1_19

}

TY - GEN

T1 - Verified error bounds for the real gamma function using double exponential formula over semi-infinite interval

AU - Yamanaka, Naoya

AU - Okayama, Tomoaki

AU - Oishi, Shinichi

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

KW - Double exponential formula

KW - Gamma function

KW - Verified bound

UR - http://www.scopus.com/inward/record.url?scp=84964059135&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84964059135&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-32859-1_19

DO - 10.1007/978-3-319-32859-1_19

M3 - Conference contribution

AN - SCOPUS:84964059135

SN - 9783319328584

VL - 9582

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 224

EP - 228

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

PB - Springer Verlag

ER -