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1: 25.6 Integer Arguments
§25.6 Integer Arguments
►§25.6(i) Function Values
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25.6.3
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§25.6(ii) Derivative Values
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25.6.19
, , .
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2: 22.3 Graphics
3: 9.7 Asymptotic Expansions
4: Bibliography B
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Algorithms for computing Bessel functions of half-integer order with complex arguments.
Zh. Vychisl. Mat. i Mat. Fiz. 28 (10), pp. 1449–1460, 1597.
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Pionic atoms.
Annual Review of Nuclear and Particle Science 20, pp. 467–508.
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A program for computing the Riemann zeta function for complex argument.
Comput. Phys. Comm. 20 (3), pp. 441–445.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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Generalized hypergeometric functions at unit argument.
Proc. Amer. Math. Soc. 114 (1), pp. 145–153.
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5: Bibliography F
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Theory and Computation of Spheroidal Harmonics with General Arguments.
Master’s Thesis, The University of Western Australia, Department of Physics.
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Weber Parabolic Cylinder Functions and Other Functions for Large Arguments.
National Physical Laboratory Mathematical Tables, Vol. 4.
Department of Scientific and Industrial Research, Her Majesty’s Stationery Office, London.
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Error bounds for the asymptotic expansion of the ratio of two gamma functions with complex argument.
SIAM J. Math. Anal. 23 (2), pp. 505–511.
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Fast computation of incomplete elliptic integral of first kind by half argument transformation.
Numer. Math. 116 (4), pp. 687–719.
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6: Software Index
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7: Bibliography D
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Recherches analytiques sur la théorie des nombres premiers. Deuxième partie. Les fonctions de Dirichlet et les nombres premiers de la forme linéaire
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Ann. Soc. Sci. Bruxelles 20, pp. 281–397 (French).
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Complex zeros of cylinder functions.
Math. Comp. 20 (94), pp. 215–222.
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Bessel functions and of integer order and complex argument.
Comput. Phys. Comm. 78 (1-2), pp. 181–189.
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Uniform asymptotic expansions for Whittaker’s confluent hypergeometric functions.
SIAM J. Math. Anal. 20 (3), pp. 744–760.
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Conical functions of purely imaginary order and argument.
Proc. Roy. Soc. Edinburgh Sect. A 143 (5), pp. 929–955.
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8: 20.11 Generalizations and Analogs
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►For relatively prime integers
with and even, the Gauss sum
is defined by
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20.11.1
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►If both are positive, then allows inversion of its arguments as a modular transformation (compare (23.15.3) and (23.15.4)):
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20.11.3
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20.11.8
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9: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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Tables of for Complex Argument.
Pergamon Press, New York.
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Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule.
Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.
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A subroutine package for Bessel functions of a complex argument and nonnegative order.
Technical Report
Technical Report SAND85-1018, Sandia National Laboratories, Albuquerque, NM.
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Spherical Bessel functions and of integer order and real argument.
Comput. Phys. Comm. 14 (3-4), pp. 261–265.
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10: Bibliography M
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The dilogarithm function for complex argument.
Proc. Roy. Soc. London Ser. A 459, pp. 2807–2819.
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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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Derivatives of the Hurwitz zeta function for rational arguments.
J. Comput. Appl. Math. 100 (2), pp. 201–206.
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The -analogue of the Laguerre polynomials.
J. Math. Anal. Appl. 81 (1), pp. 20–47.
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The dilogarithm function of a real argument.
Math. Comp. 33 (146), pp. 778–787.
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