Euler,s Hypergeometric Transformations
المؤلف:
Abramowitz, M. and Stegun, I. A.
المصدر:
Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, 9th printing. New York: Dover, 1972.
الجزء والصفحة:
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11-6-2019
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Euler's Hypergeometric Transformations
 |
(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).
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.
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