Schaar,s Identity
المؤلف:
Borwein, J. M. and Borwein, P. B.
المصدر:
Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, 1987.
الجزء والصفحة:
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25-8-2020
965
Schaar's Identity
A generalization of the Gaussian sum. For 
and 
of opposite parity (i.e., one is even and the other is odd), Schaar's identity states
Schaar's identity can also be written so as to be valid for 
, 
with 
even.
REFERENCES:
Borwein, J. M. and Borwein, P. B. Pi & the AGM: A Study in Analytic Number Theory and Computational Complexity. New York: Wiley, 1987.
Evans, R. and Berndt, B. "The Determination of Gauss Sums." Bull. Amer. Math. Soc. 5, 107-129, 1981.
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