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11—20 of 889 matching pages
11: 16.27 Software
12: 23.24 Software
13: 4.29 Graphics
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§4.29(i) Real Arguments
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►The conformal mapping is obtainable from Figure 4.15.7 by rotating both the -plane and the -plane through an angle , compare (4.28.8). ►The surfaces for the complex hyperbolic and inverse hyperbolic functions are similar to the surfaces depicted in §4.15(iii) for the trigonometric and inverse trigonometric functions. …14: 10.77 Software
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§10.77(ii) Bessel Functions–Real Argument and Integer or Half-Integer Order (including Spherical Bessel Functions)
… ►§10.77(iii) Bessel Functions–Real Order and Argument
… ►§10.77(vi) Bessel Functions–Imaginary Order and Real Argument
… ►§10.77(vii) Bessel Functions–Complex Order and Real Argument
… ►§10.77(viii) Bessel Functions–Complex Order and Argument
…15: 11.8 Analogs to Kelvin Functions
§11.8 Analogs to Kelvin Functions
►For properties of Struve functions of argument see McLachlan and Meyers (1936).16: Bibliography N
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Numerical evaluation of the confluent hypergeometric function for complex arguments of large magnitudes.
J. Comput. Appl. Math. 39 (2), pp. 193–200.
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On the large argument asymptotics of the Lommel function via Stieltjes transforms.
Asymptot. Anal. 91 (3-4), pp. 265–281.
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Error Bounds for the Large-Argument Asymptotic Expansions of the Hankel and Bessel Functions.
Acta Appl. Math. 150, pp. 141–177.
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Error bounds for the large-argument asymptotic expansions of the Lommel and allied functions.
Stud. Appl. Math. 140 (4), pp. 508–541.
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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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17: Software Index
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Open Source | With Book | Commercial | |||||||||||||||||||||||
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16.27(iii) Complex Arguments | ✓ | a | ✓ | ✓ | ✓ | ✓ | |||||||||||||||||||
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20.16(iii) Complex arguments | ✓ | a | ✓ | ✓ | ✓ | ✓ | a | ||||||||||||||||||
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22.22(iii) Complex Argument | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | ✓ | a | ✓ | |||||||||||||||
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23.24(iii) Complex Argument | ✓ | ✓ | ✓ | ✓ | a | ||||||||||||||||||||
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33.26(iii) Complex arguments | ✓ | a | ✓ | ||||||||||||||||||||||
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18: 35.2 Laplace Transform
§35.2 Laplace Transform
►Definition
… ►where the integration variable ranges over the space . … ►Inversion Formula
… ►Convolution Theorem
…19: Bibliography
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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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Algorithm 644: A portable package for Bessel functions of a complex argument and nonnegative order.
ACM Trans. Math. Software 12 (3), pp. 265–273.
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Algorithm 683: A portable FORTRAN subroutine for exponential integrals of a complex argument.
ACM Trans. Math. Software 16 (2), pp. 178–182.
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20: 10.75 Tables
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►Also, for additional listings of tables pertaining to complex arguments see Babushkina et al. (1997).
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Bickley et al. (1952) tabulates or , or , , (.01 or .1) 10(.1) 20, 8S; , , , or , 10S.
The main tables in Abramowitz and Stegun (1964, Chapter 9) give , , , , 8D–10D or 10S; , , , ; , , , 8D; , , , , 5S; , , , , 9–10S.
Kerimov and Skorokhodov (1984b) tabulates all zeros of the principal values of and , for , 9S.
Kerimov and Skorokhodov (1984c) tabulates all zeros of and in the sector for , 9S.