arguments e±iπ/3
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31—40 of 539 matching pages
31: 33.11 Asymptotic Expansions for Large
32: 19.7 Connection Formulas
33: 10.67 Asymptotic Expansions for Large Argument
§10.67 Asymptotic Expansions for Large Argument
►§10.67(i) , and Derivatives
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10.67.1
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§10.67(ii) Cross-Products and Sums of Squares in the Case
…34: 10.61 Definitions and Basic Properties
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§10.61(iii) Reflection Formulas for Arguments
►In general, Kelvin functions have a branch point at and functions with arguments are complex. … ►§10.61(iv) Reflection Formulas for Orders
… ►35: 32.1 Special Notation
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►Unless otherwise noted, primes indicate derivatives with respect to the argument.
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36: 9.1 Special Notation
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►Other notations that have been used are as follows: and for and (Jeffreys (1928), later changed to and ); , (Fock (1945)); (Szegő (1967, §1.81)); , (Tumarkin (1959)).
nonnegative integer, except in §9.9(iii). | |
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primes | derivatives with respect to argument. |
37: 35.2 Laplace Transform
§35.2 Laplace Transform
►Definition
… ►where the integration variable ranges over the space . … ►Inversion Formula
… ►Convolution Theorem
…38: Bibliography Y
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The calculation of the Riemann zeta function in the complex domain.
USSR Comput. Math. and Math. Phys. 25 (2), pp. 111–119.
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Computation of the derivatives of the Riemann zeta-function in the complex domain.
USSR Comput. Math. and Math. Phys. 28 (4), pp. 115–124.
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Computation of Kummer functions for large argument
by using the -method.
Trans. Inform. Process. Soc. Japan 36 (10), pp. 2335–2342 (Japanese).
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39: 19.6 Special Cases
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►Exact values of and for various special values of are given in Byrd and Friedman (1971, 111.10 and 111.11) and Cooper et al. (2006).
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19.6.8
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§19.6(iii)
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19.6.10
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40: Bibliography G
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Algorithm 259: Legendre functions for arguments larger than one.
Comm. ACM 8 (8), pp. 488–492.
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Some integrals involving three Bessel functions when their arguments satisfy the triangle inequalities.
J. Math. Phys. 25 (11), pp. 3350–3356.
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Evaluation of Legendre functions of argument greater than one.
Comput. Phys. Comm. 105 (2-3), pp. 273–283.
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Algorithm 831: Modified Bessel functions of imaginary order and positive argument.
ACM Trans. Math. Software 30 (2), pp. 159–164.
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Algorithm 490: The Dilogarithm function of a real argument [S22].
Comm. ACM 18 (4), pp. 200–202.
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