beta%20integrals
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1—10 of 16 matching pages
1: 9.18 Tables
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Zhang and Jin (1996, p. 337) tabulates , , , for to 8S and for to 9D.
Sherry (1959) tabulates , , , , ; 20S.
Corless et al. (1992) gives the real and imaginary parts of for ; 14S.
§9.18(v) Integrals
…2: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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Uniform asymptotic expansion for the incomplete beta function.
SIGMA Symmetry Integrability Geom. Methods Appl. 12, pp. 101, 5 pages.
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Elliptic integrals of the second and third kinds.
Zastos. Mat. 11, pp. 99–102.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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3: 20.10 Integrals
§20.10 Integrals
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20.10.4
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►For further integrals of theta functions see Erdélyi et al. (1954a, pp. 61–62 and 339), Prudnikov et al. (1990, pp. 356–358), Prudnikov et al. (1992a, §3.41), and Gradshteyn and Ryzhik (2000, pp. 627–628).
4: 8.26 Tables
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Khamis (1965) tabulates for , to 10D.
§8.26(iii) Incomplete Beta Functions
… ►Abramowitz and Stegun (1964, pp. 245–248) tabulates for , to 7D; also for , to 6S.
Pagurova (1961) tabulates for , to 4-9S; for , to 7D; for , to 7S or 7D.
Zhang and Jin (1996, Table 19.1) tabulates for , to 7D or 8S.
5: 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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Tables of the Incomplete Beta-function.
2nd edition, Published for the Biometrika Trustees at the Cambridge
University Press, Cambridge.
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A note on the computation of the incomplete beta function.
Adv. Eng. Software 12 (1), pp. 39–44.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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Elliptic integrals.
Computers in Physics 4 (1), pp. 92–96.
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6: Bibliography R
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Tablitsy modifitsirovannykh funktsii Besselya
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“Nauka”, Moscow (Russian).
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On the definition and properties of generalized - symbols.
J. Math. Phys. 20 (12), pp. 2398–2415.
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Integral representations for products of Airy functions.
Z. Angew. Math. Phys. 46 (2), pp. 159–170.
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Integral representations for products of Airy functions. II. Cubic products.
Z. Angew. Math. Phys. 48 (4), pp. 646–655.
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Dawson’s integral and the sampling theorem.
Computers in Physics 3 (2), pp. 85–87.
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7: Bibliography I
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Computation of integrals over the half-line involving products of Bessel functions, with application to microwave transmission lines.
Z. Angew. Math. Mech. 75 (12), pp. 917–926.
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An integral which occurs in statistics.
Proceedings of the Cambridge Philosophical Society 29, pp. 271–276.
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The real roots of Bernoulli polynomials.
Ann. Univ. Turku. Ser. A I 37, pp. 1–20.
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-Hermite polynomials, biorthogonal rational functions, and -beta integrals.
Trans. Amer. Math. Soc. 346 (1), pp. 63–116.
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8: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Application of the combined nonlinear-condensation transformation to problems in statistical analysis and theoretical physics.
Comput. Phys. Comm. 150 (1), pp. 1–20.
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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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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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9: Bibliography M
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Rational approximations, software and test methods for sine and cosine integrals.
Numer. Algorithms 12 (3-4), pp. 259–272.
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Algorithm AS 63. The incomplete beta integral.
Appl. Statist. 22 (3), pp. 409–411.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Hierarchies and logarithmic oscillations in the temporal relaxation patterns of proteins and other complex systems.
Proc. Nat. Acad. Sci. U .S. A. 96 (20), pp. 11085–11089.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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