Riemann P-Differential Equation

The differential equation

where

first obtained in the form by Papperitz (1885; Barnes 1908). Solutions are Riemann P-series (Abramowitz and Stegun 1972, pp. 564-565). Zwillinger (1995, p. 414) confusingly calls this equation the "hypergeometric equation."

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.

Barnes, E. W. "A New Development in the Theory of the Hypergeometric Functions." Proc. London Math. Soc. 6, 141-177, 1908.

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

Papperitz. Math. Ann. 25, 213, 1885.

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

Zwillinger, D. Handbook of Differential Equations, 3rd ed. Boston, MA: Academic Press, p. 126, 1997.