Tokyo Journal of Mathematics

Zeta Regularized Product Expressions for Multiple Trigonometric Functions

Nobushige KUROKAWA and Masato WAKAYAMA

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We introduce a multiple analogue of the gamma function which differs from the one defined by Barnes [B]. Using this function, we give expressions of the multiple sine and cosine functions in terms of zeta regularized products. The expression of the multiple sine function can be interpreted as a reflection formula of this new multiple analogue of the gamma function.

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Tokyo J. Math., Volume 27, Number 2 (2004), 469-480.

First available in Project Euclid: 5 June 2009

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Zentralblatt MATH identifier

Primary: 11M36: Selberg zeta functions and regularized determinants; applications to spectral theory, Dirichlet series, Eisenstein series, etc. Explicit formulas
Secondary: 11M06: $\zeta (s)$ and $L(s, \chi)$


KUROKAWA, Nobushige; WAKAYAMA, Masato. Zeta Regularized Product Expressions for Multiple Trigonometric Functions. Tokyo J. Math. 27 (2004), no. 2, 469--480. doi:10.3836/tjm/1244208402.

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