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发表于 2025-3-21 17:54:57
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同音
发表于 2025-3-21 22:00:13
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maroon
发表于 2025-3-22 01:52:54
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condone
发表于 2025-3-22 04:40:43
Problems in Diophantine Approximation,related to Ramanujan’s only publication in the subject, a problem that he published in the .. In this partial manuscript, Ramanujan provides the best Diophantine approximation to e, approximately 60 years before the theorem was rediscovered and proved in print.
无辜
发表于 2025-3-22 11:37:59
A Partial Manuscript on Fourier and Laplace Transforms, one of the highlights of the book, a beautiful new transformation formula involving the logarithmic derivative of the gamma function. An extremely clever device used to prove this transformation formula harkens back to Ramanujan’s paper, ..
遭遇
发表于 2025-3-22 16:35:20
Integral Analogues of Theta Functions and Gauss Sums,sfies a transformation formula similar to that satisfied by the classical theta functions. The integral can also be thought of as an analogue of Gauss sums or as an analogue of the classical Weierstrass σ-function.
pacific
发表于 2025-3-22 20:30:59
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能得到
发表于 2025-3-22 22:22:25
,Koshliakov’s Formula and Guinand’s Formula,In this chapter, we relate two well-known identities, with the names of N.S. Koshliakov and A.P. Guinand attached to them, which were proved by Ramanujan and recorded in his lost notebook before their discoveries by the aforementioned mathematicians. Ramanujan also derived some related formulas that have not been rediscovered by others.
capsaicin
发表于 2025-3-23 03:03:41
Theorems Featuring the Gamma Function,Some integrals of gamma functions are evaluated. A remarkable approximation to the gamma function, with a slightly less precise approximation submitted as a problem by Ramanujan to the ., is examined in detail.
Definitive
发表于 2025-3-23 07:54:55
Hypergeometric Series,Two fascinating formulas for bilateral hypergeometric series are proved. The second portion of the chapter is devoted to a beautiful continued fraction related to hypergeometric polynomials.