Ramanujan beta integral
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8 matching pages
1: 5.13 Integrals
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Ramanujan’s Beta Integral
…2: Bibliography P
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Orthogonal polynomials and some -beta integrals of Ramanujan.
J. Math. Anal. Appl. 112 (2), pp. 517–540.
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3: 17.13 Integrals
§17.13 Integrals
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17.13.2
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Ramanujan’s Integrals
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17.13.3
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►Askey (1980) conjectured extensions of the foregoing integrals that are closely related to Macdonald (1982).
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4: Bibliography R
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Congruence properties of partitions.
Math. Z. 9 (1-2), pp. 147–153.
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Some properties of Bernoulli’s numbers (J. Indian Math. Soc. 3 (1911), 219–234.).
In Collected Papers,
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Collected Papers of Srinivasa Ramanujan.
Chelsea Publishing Co., New York.
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Tablitsy modifitsirovannykh funktsii Besselya
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“Nauka”, Moscow (Russian).
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Dawson’s integral and the sampling theorem.
Computers in Physics 3 (2), pp. 85–87.
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5: Bibliography C
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Calcolo delle funzioni speciali , , , , alle alte precisioni.
Atti Accad. Sci. Lett. Arti Palermo Ser. (5) 2(1981/82) (1), pp. 7–25 (Italian).
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On Ramanujan’s cubic transformation formula for
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Math. Proc. Cambridge Philos. Soc. 124 (2), pp. 193–204.
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Algorithm AS 310. Computing the non-central beta distribution function.
Appl. Statist. 46 (1), pp. 146–156.
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Approximations and Complex Multiplication According to Ramanujan.
In Ramanujan Revisited (Urbana-Champaign, Ill., 1987), G. E. Andrews, R. A. Askey, B. C. Bernd, K. G. Ramanathan, and R. A. Rankin (Eds.),
pp. 375–472.
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Integrals involving complete elliptic integrals.
J. Comput. Appl. Math. 106 (1), pp. 169–175.
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6: Bibliography K
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On an integral of Hardy and Littlewood.
Kyushu J. Math. 52 (1), pp. 249–263.
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Asymptotic expansions of certain -series and a formula of Ramanujan for specific values of the Riemann zeta function.
Acta Arith. 107 (3), pp. 269–298.
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Comment on “The incomplete beta function law for parallel tempering sampling of classical canonical systems” [J. Chem. Phys. 120, 4119 (2004)].
J. Chem. Phys. 121 (2), pp. 1167.
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Orthogonal polynomials with weight function
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Canad. Math. Bull. 27 (2), pp. 205–214.
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The Askey scheme as a four-manifold with corners.
Ramanujan J. 20 (3), pp. 409–439.
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7: Bibliography D
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Integral Transforms and their Applications.
2nd edition, Applied Mathematical Sciences, Vol. 25, Springer-Verlag, New York.
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Integral transforms and their applications.
Third edition, CRC Press, Boca Raton, FL.
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Algorithm 708: Significant digit computation of the incomplete beta function ratios.
ACM Trans. Math. Software 18 (3), pp. 360–373.
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Ramanujan’s master theorem for symmetric cones.
Pacific J. Math. 175 (2), pp. 447–490.
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The incomplete beta function—a historical profile.
Arch. Hist. Exact Sci. 24 (1), pp. 11–29.
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8: Bibliography
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Chapter of Ramanujan’s second notebook: Theta-functions and -series.
Mem. Amer. Math. Soc. 53 (315), pp. v+85.
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A -beta integral on the unit circle and some biorthogonal rational functions.
Proc. Amer. Math. Soc. 121 (2), pp. 553–561.
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Gauss, Landen, Ramanujan, the arithmetic-geometric mean, ellipses, , and the Ladies Diary.
Amer. Math. Monthly 95 (7), pp. 585–608.
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Ramanujan Revisited.
Academic Press Inc., Boston, MA.
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Multiple series Rogers-Ramanujan type identities.
Pacific J. Math. 114 (2), pp. 267–283.
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