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单词 Ramanujan 6-10-8 Identity
释义

Ramanujan 6-10-8 Identity

Let , then

(1)
This can also be expressed by defining
(2)
(3)
Then
(4)

and identity (1) can then be written
(5)

Incidentally,
(6)
(7)


References

Berndt, B. C. Ramanujan's Notebooks, Part IV. New York: Springer-Verlag, pp. 3 and 102-106, 1994.

Berndt, B. C. and Bhargava, S. ``A Remarkable Identity Found in Ramanujan's Third Notebook.'' Glasgow Math. J. 34, 341-345, 1992.

Berndt, B. C. and Bhargava, S. ``Ramanujan--For Lowbrows.'' Amer. Math. Monthly 100, 644-656, 1993.

Bhargava, S. ``On a Family of Ramanujan's Formulas for Sums of Fourth Powers.'' Ganita 43, 63-67, 1992.

Hirschhorn, M. D. ``Two or Three Identities of Ramanujan.'' Amer. Math. Monthly 105, 52-55, 1998.

Nanjundiah, T. S. ``A Note on an Identity of Ramanujan.'' Amer. Math. Monthly 100, 485-487, 1993.

Ramanujan, S. Notebooks. New York: Springer-Verlag, pp. 385-386, 1987.


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