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1—10 of 597 matching pages
1: Bibliography H
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The Laplace transform for expressions that contain a probability function.
Bul. Akad. Štiince RSS Moldoven. 1973 (2), pp. 78–80, 93 (Russian).
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Integrals containing the Fresnel functions and
.
Bul. Akad. Štiince RSS Moldoven. 1975 (3), pp. 48–60, 93 (Russian).
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Lamé polynomials of large order.
SIAM J. Math. Anal. 8 (5), pp. 800–842.
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Calculation of Coulomb wave functions for high energies.
Phys. Rev. 54 (8), pp. 627–628.
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Coulomb Wave Functions.
In Handbuch der Physik, Bd. 41/1, S. Flügge (Ed.),
pp. 408–465.
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2: Bibliography D
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The principal frequencies of vibrating systems with elliptic boundaries.
Quart. J. Mech. Appl. Math. 8 (3), pp. 361–372.
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Handbuch der Laplace-Transformation. Bd. II. Anwendungen der Laplace-Transformation. 1. Abteilung.
Birkhäuser Verlag, Basel und Stuttgart (German).
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Inequalities for extreme zeros of some classical orthogonal and -orthogonal polynomials.
Math. Model. Nat. Phenom. 8 (1), pp. 48–59.
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Lamé instantons.
J. High Energy Phys. 2000 (1), pp. Paper 19, 8.
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Uniform asymptotic expansions for Charlier polynomials.
J. Approx. Theory 112 (1), pp. 93–133.
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3: 27.2 Functions
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27.2.9
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►It is the special case of the function that counts the number of ways of expressing as the product of factors, with the order of factors taken into account.
…Note that .
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►Table 27.2.2 tabulates the Euler totient function , the divisor function (), and the sum of the divisors (), for .
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4: Bibliography
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Tables of for Complex Argument.
Pergamon Press, New York.
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Supplement to a paper “On the intensity of light in the neighbourhood of a caustic”.
Trans. Camb. Phil. Soc. 8, pp. 595–599.
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Frequency response characteristics of the multiport planar elliptic patch.
IEEE Trans. Microwave Theory Tech. 40 (8), pp. 1726–1730.
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Algorithm 511: CDC 6600 subroutines IBESS and JBESS for Bessel functions and , ,
.
ACM Trans. Math. Software 3 (1), pp. 93–95.
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Special Functions.
Encyclopedia of Mathematics and its Applications, Vol. 71, Cambridge University Press, Cambridge.
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5: 7.14 Integrals
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7.14.1
, .
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7.14.5
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7.14.7
,
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►For collections of integrals see Apelblat (1983, pp. 131–146), Erdélyi et al. (1954a, vol. 1, pp. 40, 96, 176–177), Geller and Ng (1971), Gradshteyn and Ryzhik (2000, §§5.4 and 6.28–6.32), Marichev (1983, pp. 184–189), Ng and Geller (1969), Oberhettinger (1974, pp. 138–139, 142–143), Oberhettinger (1990, pp. 48–52, 155–158), Oberhettinger and Badii (1973, pp. 171–172, 179–181), Prudnikov et al. (1986b, vol. 2, pp. 30–36, 93–143), Prudnikov et al. (1992a, §§3.7–3.8), and Prudnikov et al. (1992b, §§3.7–3.8).
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6: 3.9 Acceleration of Convergence
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►For further information on the epsilon algorithm see Brezinski and Redivo Zaglia (1991, pp. 78–95).
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Table 3.9.1: Shanks’ transformation for .
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4 | 0.82221 76684 88 | 0.82246 28314 41 | 0.82246 69467 93 | 0.82246 70314 36 | 0.82246 70333 75 |
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8 | 0.82243 73137 33 | 0.82246 67719 32 | 0.82246 70301 49 | 0.82246 70333 73 | 0.82246 70334 23 |
9 | 0.82248 70624 89 | 0.82246 71865 91 | 0.82246 70351 34 | 0.82246 70334 48 | 0.82246 70334 24 |
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7: Bibliography T
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LSFBTR: A subroutine for calculating spherical Bessel transforms.
Comput. Phys. Comm. 30 (1), pp. 93–99.
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A set of algorithms for the incomplete gamma functions.
Probab. Engrg. Inform. Sci. 8, pp. 291–307.
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Bernoulli polynomials old and new: Generalizations and asymptotics.
CWI Quarterly 8 (1), pp. 47–66.
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The lemniscate constants.
Comm. ACM 18 (1), pp. 14–19.
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Hyperspherical elliptic harmonics and their relation to the Heun equation.
Phys. Rev. A 63 (032510), pp. 1–8.
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8: Bibliography M
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On the evaluation of indefinite integrals involving the special functions: Application of method.
Quart. Appl. Math. 13, pp. 84–93.
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Inequalities for the zeros of Bessel functions.
SIAM J. Math. Anal. 8 (1), pp. 166–170.
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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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Balanced summation theorems for basic hypergeometric series.
Adv. Math. 131 (1), pp. 93–187.
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On the representation of numbers as a sum of squares.
Quarterly Journal of Math. 48, pp. 93–104.
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9: Bibliography O
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Hyperterminants. II.
J. Comput. Appl. Math. 89 (1), pp. 87–95.
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Uniform asymptotic expansions for hypergeometric functions with large parameters. III.
Analysis and Applications (Singapore) 8 (2), pp. 199–210.
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Connection formulas for second-order differential equations with multiple turning points.
SIAM J. Math. Anal. 8 (1), pp. 127–154.
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Connection formulas for second-order differential equations having an arbitrary number of turning points of arbitrary multiplicities.
SIAM J. Math. Anal. 8 (4), pp. 673–700.
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Numerical evaluation of the dilogarithm of complex argument.
Celestial Mech. Dynam. Astronom. 62 (1), pp. 93–98.
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10: Bibliography C
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Generalized hypergeometric functions and the evaluation of scalar one-loop integrals in Feynman diagrams.
J. Comput. Appl. Math. 115 (1-2), pp. 93–99.
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Elliptic integrals of the first kind.
SIAM J. Math. Anal. 8 (2), pp. 231–242.
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Expansions in terms of parabolic cylinder functions.
Proc. Edinburgh Math. Soc. (2) 8, pp. 50–65.
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Coulomb phase shift.
American Journal of Physics 47 (8), pp. 683–684.
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Inverse Acoustic and Electromagnetic Scattering Theory.
2nd edition, Applied Mathematical Sciences, Vol. 93, Springer-Verlag, Berlin.
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