A generalization of the Riemann Zeta Function with a Formula
(1) |
(2) |
(3) |
(4) |
(5) | |||
(6) | |||
(7) |
(8) |
For Positive integers , , and ,
(9) |
(10) | |
(11) | |
(12) | |
(13) |
See also Khintchine's Constant, Polygamma Function, Psi Function, Riemann Zeta Function, Zeta Function
References
Apostol, T. M. Introduction to Analytic Number Theory. New York: Springer-Verlag, 1995.
Elizalde, E.; Odintsov, A. D.; and Romeo, A. Zeta Regularization Techniques with Applications.
River Edge, NJ: World Scientific, 1994.
Knopfmacher, J. ``Generalised Euler Constants.'' Proc. Edinburgh Math. Soc. 21, 25-32, 1978.
Magnus, W. and Oberhettinger, F. Formulas and Theorems for the Special Functions of Mathematical Physics, 3rd ed.
New York: Springer-Verlag, 1966.
Miller, J. and Adamchik, V. ``Derivatives of the Hurwitz Zeta Function for Rational Arguments.'' Submitted to
J. Symb. Comput.
Spanier, J. and Oldham, K. B. ``The Hurwitz Function .''
Ch. 62 in An Atlas of Functions.
Washington, DC: Hemisphere, pp. 653-664, 1987.
Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University
Press, pp. 268-269, 1950.
© 1996-9 Eric W. Weisstein