Legendre polynomials and Ramanujan-type series for 1/π
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We resolve a family of recently observed identities involving 1/π using the theory of modular forms and hypergeometric series. In particular, we resort to a formula of Brafman which relates a generating function of the Legendre polynomials to a product of two Gaussian hypergeometric functions. Using our methods, we also derive some new Ramanujan-type series.
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- Legendre polynomials and Ramanujan-type series for 1/π
Israel Journal of Mathematics
Volume 194, Issue 1 , pp 183-207
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- 181. Department of Mathematics, National University of Singapore, 2 Science Drive 2, Singapore, 117543, Singapore
- 281. School of Mathematical and Physical Sciences, The University of Newcastle, Callaghan, NSW, 2308, Australia