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
where
|
(6)
|
See also
Riemann P-Differential
Equation
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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.Referenced on Wolfram|Alpha
Riemann P-Series
Cite this as:
Weisstein, Eric W. "Riemann P-Series."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/RiemannP-Series.html
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