|
(1)
|
where is a hypergeometric
function. The solution can be written using the Euler's transformations
in the equivalent forms
Equation (7) gives Euler's convergence improvement transform of the series (Abramowitz and Stegun 1972, p. 555).
See also
Euler Transform,
Hypergeometric
Function
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References
Abramowitz, M. and Stegun, I. A. (Eds.). Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing.
New York: Dover, 1972.Euler, L. Nova Acta Acad. Petropol. 7,
p. 58, 1778.Morse, P. M. and Feshbach, H. Methods
of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 585-591,
1953.Referenced on Wolfram|Alpha
Euler's Hypergeometric
Transformations
Cite this as:
Weisstein, Eric W. "Euler's Hypergeometric Transformations." From MathWorld--A Wolfram Web Resource.
https://mathworld.wolfram.com/EulersHypergeometricTransformations.html
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