Riemann P-Series

The solutions to the Riemann P-differential equation are known as the Riemann -series, or sometimes the Riemann -function, given by

(1)

Solutions are given in terms of the hypergeometric function by

			(2)
			(3)
			(4)
			(5)

where

(6)

REFERENCES:

Abramowitz, M. and Stegun, I. A. (Eds.). "Riemann's Differential Equation." §15.6 in Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, pp. 564-565, 1972.

Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 541-543, 1953.

Riemann, B. Abh. d. Ges. d. Wiss. zu Göttingen 7, 1857. Reprinted in Mathematisch Werke, p. 67, 1892.

Whittaker, E. T. and Watson, G. N. A Course in Modern Analysis, 4th ed. Cambridge, England: Cambridge University Press, pp. 283-284, 1990.

Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, p. 414, 1995.