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Ramanujan’s unpublished manuscript on the partition and tau functions with proofs and commentary
 Sém. Lotharingien de Combinatoire 42 (1999), 63 pp.; in The Andrews Festschrift
, 2001
"... When Ramanujan died in 1920, he left behind an incomplete, unpublished manuscript in two parts on the partition function p(n) and, in contemporary terminology, Ramanujan’s taufunction τ(n). The first part, beginning with the Roman numeral I, is written on 43 pages, with the last nine comprising mat ..."
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Cited by 31 (13 self)
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When Ramanujan died in 1920, he left behind an incomplete, unpublished manuscript in two parts on the partition function p(n) and, in contemporary terminology, Ramanujan’s taufunction τ(n). The first part, beginning with the Roman numeral I, is written on 43 pages, with the last nine comprising material for insertion in the
Algebraic transformations of Gauss hypergeometric functions, preprint
, 2004
"... The paper classifies algebraic transformations of Gauss hypergeometric functions and pullback transformations between hypergeometric differential equations. This classification recovers the classical transformations of degree 2, 3, 4, 6, and finds other transformations of some special classes of th ..."
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Cited by 22 (9 self)
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The paper classifies algebraic transformations of Gauss hypergeometric functions and pullback transformations between hypergeometric differential equations. This classification recovers the classical transformations of degree 2, 3, 4, 6, and finds other transformations of some special classes of the Gauss hypergeometric function.
Generalized elliptic integrals and modular equations
 Pacific J. Math
"... In geometric function theory, generalized elliptic integrals and functions arise from the SchwarzChristoffel transformation of the upper halfplane onto a parallelogram and are naturally related to Gaussian hypergeometric functions. Certain combinations of these integrals also occur in analytic num ..."
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Cited by 21 (8 self)
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In geometric function theory, generalized elliptic integrals and functions arise from the SchwarzChristoffel transformation of the upper halfplane onto a parallelogram and are naturally related to Gaussian hypergeometric functions. Certain combinations of these integrals also occur in analytic number theory in the study of Ramanujan’s modular equations and approximations to π. The authors study the monotoneity and convexity properties of these quantities and obtain sharp inequalities for them. 1. Introduction. In 1995 B. Berndt, S. Bhargava, and F. Garvan published an important paper [BBG] in which they studied generalized modular equations and gave proofs for numerous statements concerning these equations made by Ramanujan in his unpublished notebooks. No record of Ramanujan’s original
New 5F4 hypergeometric transformations, threevariable Mahler measures, and formulas for 1/π
 Ramanujan J
"... New relations are established between families of threevariable Mahler measures. Those identities are then expressed as transformations for the 5F4 hypergeometric function. We use these results to obtain two explicit 5F4 evaluations, and several new formulas for 1/π. MSC: 33C20, 33C05, 11F66 1 ..."
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Cited by 18 (7 self)
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New relations are established between families of threevariable Mahler measures. Those identities are then expressed as transformations for the 5F4 hypergeometric function. We use these results to obtain two explicit 5F4 evaluations, and several new formulas for 1/π. MSC: 33C20, 33C05, 11F66 1
Ramanujan’s series for 1/π: A survey
"... Beginning with Ramanujan’s epic paper, Modular Equations and Approximations to π, we describe Ramanujan’s series for 1/π and later attempts to prove them. Generalizations, analogues, and consequences of Ramanujan’s series are discussed. ..."
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Cited by 15 (2 self)
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Beginning with Ramanujan’s epic paper, Modular Equations and Approximations to π, we describe Ramanujan’s series for 1/π and later attempts to prove them. Generalizations, analogues, and consequences of Ramanujan’s series are discussed.
Ramanujan's Explicit Values For The Classical ThetaFunction
"... this paper is to prove each of these new evaluations. We also establish some new evaluations of '(q) ..."
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Cited by 10 (7 self)
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this paper is to prove each of these new evaluations. We also establish some new evaluations of '(q)
Cubic modular equations and new Ramanujantype series for 1/π
 Pacific J. Math
"... In this paper, we derive new Ramanujantype series for 1/π which belong to “Ramanujan’s theory of elliptic functions to alternative base 3 ” developed recently by B.C. Berndt, S. Bhargava, and F.G. Garvan. 1. Introduction. Let (a)0 = 1 and, for a positive integer m, (a)m: = a(a + 1)(a +2)···(a+m−1), ..."
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Cited by 10 (2 self)
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In this paper, we derive new Ramanujantype series for 1/π which belong to “Ramanujan’s theory of elliptic functions to alternative base 3 ” developed recently by B.C. Berndt, S. Bhargava, and F.G. Garvan. 1. Introduction. Let (a)0 = 1 and, for a positive integer m, (a)m: = a(a + 1)(a +2)···(a+m−1), and ∞ ∑ (a)m(b)m z
Ramanujan’s series for 1/π arising from his cubic and quartic theories of elliptic functions
 J. Math. Anal. Appl
"... Abstract. Using certain representations for Eisenstein series, we derive several of Ramanujan’s series for 1/π arising from his cubic and quartic theories of elliptic functions. ..."
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Cited by 10 (4 self)
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Abstract. Using certain representations for Eisenstein series, we derive several of Ramanujan’s series for 1/π arising from his cubic and quartic theories of elliptic functions.
Generalized elliptic integrals
, 2004
"... Jacobi’s elliptic integrals and elliptic functions arise naturally from the SchwarzChristoffel conformal transformation of the upper half plane onto a rectangle. In this paper we study generalized elliptic integrals which arise from the analogous mapping of the upper half plane onto a quadrilateral ..."
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Cited by 8 (5 self)
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Jacobi’s elliptic integrals and elliptic functions arise naturally from the SchwarzChristoffel conformal transformation of the upper half plane onto a rectangle. In this paper we study generalized elliptic integrals which arise from the analogous mapping of the upper half plane onto a quadrilateral and obtain sharp monotonicity and convexity properties for certain combinations of these integrals, thus generalizing analogous wellknown results for classical conformal capacity and quasiconformal distortion functions.