Tokyo Journal of Mathematics

Bicomplex Polygamma Function

Ritu GOYAL

Full-text: Open access

Abstract

The aim of this paper is to extend the domain of polygamma function from the set of complex numbers to the set of bicomplex numbers. We also discuss integral representation, recurrence relation, multiplication formula and reflection formula for this function.

Article information

Source
Tokyo J. of Math. Volume 30, Number 2 (2007), 523-530.

Dates
First available in Project Euclid: 4 February 2008

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1202136693

Digital Object Identifier
doi:10.3836/tjm/1202136693

Mathematical Reviews number (MathSciNet)
MR2376526

Zentralblatt MATH identifier
1153.33001

Citation

GOYAL, Ritu. Bicomplex Polygamma Function. Tokyo J. of Math. 30 (2007), no. 2, 523--530. doi:10.3836/tjm/1202136693. https://projecteuclid.org/euclid.tjm/1202136693


Export citation

References

  • Adesi V.B. and Zerbini S., Analytic continuation of the Hurwitz zeta function with physical application, J. Math. Phys., 43 (2002), 3759–3765.
  • Arfken, G., Digamma and Polygamma Functions in, Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, 1985, 549–555.
  • Erdelyi, A. et al., Higher Transdendental Functions-I, McGraw-Hill, New York, 1953.
  • Goyal S.P. and Goyal R., On bicomplex Hurwitz Zeta function, South East Asian J. Math. Math. Sci. (To, appear).
  • Goyal S.P., Mathur T. and Goyal R., Bicomplex Gamma and Beta functions, J. Raj. Acad. Phy. Sci., 5 (1) (2006), 131–142.
  • Grossman, N., Polygamma functions of arbitrary order, SIAM J. Math. Anal., 7 (1976), 366–372.
  • Price G.B., An Introduction to Multicomplex Spaces and Functions, Marcel Dekker, New York, 1991.
  • Rönn S., Bicomplex algebra and function theory, Preprint: http://arXiv.org/abs/mth/0101200v1.
  • Segre C., Le rappresentazioni reali delle forme complesse e gli enti iperalgebrici, Math. Ann., 40 (1892), 413–467.