argument%20principle

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21: Bibliography N

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Algorithm 707: CONHYP: A numerical evaluator of the confluent hypergeometric function for complex arguments of large magnitudes. ACM Trans. Math. Software 18 (3), pp. 345–349.

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Notes:

Double-precision Fortran, minimum accuracy 9S, maximum accuracy 13S.

External Links:

ISSN 0098-3500, Document, GAMS (module 707; package TOMS), ZentralBlatt

Referenced by:

1st item.

Encodings:

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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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Notes:

Extended-precision Fortran evaluator, minimum accuracy 9S, maximum accuracy 13S.

External Links:

ISSN 0377-0427, Document, MathReview Entry, ZentralBlatt

Referenced by:

§13.32(iii).

Encodings:

BibTeX

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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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External Links:

ISSN 0921-7134, Document, MathReview Entry, ZentralBlatt

Referenced by:

§11.6(iii), §11.6(iii), §11.9(iii), §11.9(iii).

Encodings:

BibTeX

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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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External Links:

ISSN 0167-8019, Document, MathReview Entry, ZentralBlatt

Referenced by:

(9.7.16), (9.7.17), §9.7(iii), §9.7(iv).

Encodings:

BibTeX

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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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External Links:

ISSN 0022-2526, Document, Link, MathReview (Pedro J. Pagola), ZentralBlatt

Referenced by:

§11.11(i), §11.11(i).

Encodings:

BibTeX

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22: 4.29 Graphics

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§4.29(i) Real Arguments

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Figure 4.29.6: Principal values of $\mathrm{arccsch}x$ and $\mathrm{arcsech}x$. … Magnify

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§4.29(ii) Complex Arguments

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23: 16.27 Software

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§16.27(ii) Real Argument and Parameters

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§16.27(iii) Complex Argument and/or Parameters

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24: 23.24 Software

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§23.24(ii) Real Argument

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§23.24(iii) Complex Argument

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25: 4.3 Graphics

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§4.3(i) Real Arguments

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Figure 4.3.1: $\ln x$ and ${\mathrm{e}}^x$. … Magnify

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§4.3(ii) Complex Arguments: Conformal Maps

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§4.3(iii) Complex Arguments: Surfaces

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Figure 4.3.3: $\ln \left(x+\mathrm{i}y\right)$ (principal value). … Magnify 3D Help

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26: 10.77 Software

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§10.77(ii) Bessel Functions–Real Argument and Integer or Half-Integer Order (including Spherical Bessel Functions)

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§10.77(iii) Bessel Functions–Real Order and Argument

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§10.77(vi) Bessel Functions–Imaginary Order and Real Argument

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§10.77(vii) Bessel Functions–Complex Order and Real Argument

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§10.77(viii) Bessel Functions–Complex Order and Argument

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27: 20 Theta Functions

Chapter 20 Theta Functions

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28: 32.1 Special Notation

… ►Unless otherwise noted, primes indicate derivatives with respect to the argument. …

29: 11.8 Analogs to Kelvin Functions

§11.8 Analogs to Kelvin Functions

►For properties of Struve functions of argument $x{\mathrm{e}}^{\pm 3\pi \mathrm{i}/4}$ see McLachlan and Meyers (1936).

30: 35.2 Laplace Transform

§35.2 Laplace Transform

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Definition

… ►where the integration variable $𝐗$ ranges over the space $𝛀$. … ►

Inversion Formula

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Convolution Theorem

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