Proceedings of the Japan Academy, Series A, Mathematical Sciences

Taylor series for the reciprocal gamma function and multiple zeta values

Mika Sakata

Full-text: Open access

Abstract

We give a purely algebraic proof of a formula for Taylor coefficients of the reciprocal gamma function. The formula expresses each coefficient in terms of multiple zeta values. Our proof uses Hoffman’s harmonic algebra of multiple zeta values.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci. Volume 93, Number 6 (2017), 47-49.

Dates
First available in Project Euclid: 2 June 2017

Permanent link to this document
http://projecteuclid.org/euclid.pja/1496369013

Digital Object Identifier
doi:10.3792/pjaa.93.47

Subjects
Primary: 11M32: Multiple Dirichlet series and zeta functions and multizeta values

Keywords
Multiple zeta value gamma function

Citation

Sakata, Mika. Taylor series for the reciprocal gamma function and multiple zeta values. Proc. Japan Acad. Ser. A Math. Sci. 93 (2017), no. 6, 47--49. doi:10.3792/pjaa.93.47. http://projecteuclid.org/euclid.pja/1496369013.


Export citation

References

  • T. Arakawa and M. Kaneko, Introduction to multiple zeta values (in Japanese), MI Lecture Note Series 23 (2010), 1–111.
  • M. E. Hoffman, The algebra of multiple harmonic series, J. Algebra 194 (1997), no. 2, 477–495.
  • K. Ihara, M. Kaneko and D. Zagier, Derivation and double shuffle relations for multiple zeta values, Compos. Math. 142 (2006), no. 2, 307–338.
  • G. Racinet, Doubles mélanges des polylogarithmes multiples aux racines de l'unité, Publ. Math. Inst. Hautes Études Sci. 95 (2002), 185–231.