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Euler's integrals and multiple sine functions

Author(s): Shin-ya Koyama; Nobushige Kurokawa
Journal: Proc. Amer. Math. Soc. 133 (2005), 1257-1265.
MSC (2000): Primary 11M06
Posted: December 15, 2004
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Abstract | References | Similar articles | Additional information

Abstract: We show that Euler's famous integrals whose integrands contain the logarithm of the sine function are expressed via multiple sine functions.

References:

[E1]
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L. Euler ``Exercitationes analyticae'' Novi commentarii academiae scientiarum Petropolitanae 17 (1772) 173-204 [Opera Omnia I-15, pp.131-167].

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L. Euler ``Remarques sur un beau rapport entre les séries des puissances tant directes que réciproques" Mémoires de l'académie des sciences de Berlin 17 (1761) 83-106 (Lu en 1749) [Opera Omnia I-15, pp. 70-90].

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N. Kurokawa ``Multiple zeta functions: an example'' Adv. Stud. in Pure Math. 21 (1992) 219-226. MR 1210791 (94f:11084)

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N. Kurokawa and S. Koyama ``Multiple sine functions'' Forum Math. 15 (2003) 839-876. MR 2010282 (2004g:11077)

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S. Koyama and N. Kurokawa ``Kummer's formula for multiple gamma functions'' J. Ramanujan Math. Soc. 18 (2003) 87-107. MR 1966530 (2004a:33003)

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Additional Information:

Shin-ya Koyama
Affiliation: 2-5-27 Hayabuchi, Tsuzuki-ku, Yokohama 224-0025, Japan
Email: koyama@tmtv.ne.jp

Nobushige Kurokawa
Affiliation: Department of Mathematics, Tokyo Institute of Technology, 152-8551, Tokyo, Japan
Email: kurokawa@math.titech.ac.jp

DOI: 10.1090/S0002-9939-04-07863-3
PII: S 0002-9939(04)07863-3
Received by editor(s): August 4, 2003
Posted: December 15, 2004
Communicated by: David E. Rohrlich
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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