Ramanujan,s Sum Identity
المؤلف:
Hirschhorn, M. D.
المصدر:
"An Amazing Identity of Ramanujan." Math. Mag. 68
الجزء والصفحة:
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18-7-2020
781
Ramanujan's Sum Identity
Given the generating functions defined by
(OEIS A051028, A051029, and A051030), then
 |
(4)
|
Hirschhorn (1995) showed that
where
Hirschhorn (1996) showed that checking the first seven cases 
to 6 is sufficient to prove the result.
REFERENCES:
Hirschhorn, M. D. "An Amazing Identity of Ramanujan." Math. Mag. 68, 199-201, 1995.
Hirschhorn, M. D. "A Proof in the Spirit of Zeilberger of an Amazing Identity of Ramanujan." Math. Mag. 69, 267-269, 1996.
Sloane, N. J. A. Sequences A051028, A051029, and A051030 in "The On-Line Encyclopedia of Integer Sequences."
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