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21—30 of 311 matching pages
21: Bibliography O
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Complete elliptic integrals resulting from infinite integrals of Bessel functions.
J. Res. Nat. Bur. Standards Sect. B 78B (3), pp. 113–135.
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Complete elliptic integrals resulting from infinite integrals of Bessel functions. II.
J. Res. Nat. Bur. Standards Sect. B 79B (3-4), pp. 137–170.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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Second-order differential equations with fractional transition points.
Trans. Amer. Math. Soc. 226, pp. 227–241.
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A closed form solution of the -wave Bethe-Goldstone equation with an infinite repulsive core.
J. Math. Phys. 27 (4), pp. 1154–1158.
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22: 24.20 Tables
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►Wagstaff (1978) gives complete prime factorizations of and for and , respectively.
In Wagstaff (2002) these results are extended to and , respectively, with further complete and partial factorizations listed up to and , respectively.
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23: 4.11 Sums
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►For infinite series involving logarithms and/or exponentials, see Gradshteyn and Ryzhik (2000, Chapter 1), Hansen (1975, §44), and Prudnikov et al. (1986a, Chapter 5).
24: 25.6 Integer Arguments
25: 8 Incomplete Gamma and Related
Functions
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26: 28 Mathieu Functions and Hill’s Equation
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27: 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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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Infinite families of exact sums of squares formulas, Jacobi elliptic functions, continued fractions, and Schur functions.
Ramanujan J. 6 (1), pp. 7–149.
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New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function.
Proc. Nat. Acad. Sci. U.S.A. 93 (26), pp. 15004–15008.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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28: 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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There are infinitely many Carmichael numbers.
Ann. of Math. (2) 139 (3), pp. 703–722.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Table of Definite and Infinite Integrals.
Physical Sciences Data, Vol. 13, Elsevier Scientific Publishing Co., Amsterdam.
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29: 8.17 Incomplete Beta Functions
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§8.17(v) Continued Fraction
… ►For sums of infinite series whose terms involve the incomplete beta function see Hansen (1975, §62). … ►
8.17.24
positive integers; .
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