argument principle

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1: 1.10 Functions of a Complex Variable

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Phase (or Argument) Principle

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2: 18.39 Applications in the Physical Sciences

… ►which is the quantum superposition principle. … … ►argument a) The Harmonic Oscillator … ►argument … ►where $n$ is now the Bohr Principle Quantum Number. …

3: 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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Notes:

Contains Mathematica package for spheroidal wave functions of complex arguments with complex parameters.

External Links:

FullText

Referenced by:

§30.12, 1st item, 2nd item.

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BibTeX

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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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External Links:

MathReview (L. J. Slater), ZentralBlatt

Referenced by:

3rd item, 2nd item.

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BibTeX

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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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External Links:

ISSN 0036-1410, Document, FullText, MathReview (A. Reinfelds), ZentralBlatt

Referenced by:

§5.11(iii), §5.11(iii).

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BibTeX

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Principles and Techniques of Applied Mathematics. Dover, New York.

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Notes:

Reprint of First Edition, 1956, John-Wiley: New York

External Links:

ISBN 0-486-66444-9, MathReview Entry

Referenced by:

§1.16(ix), §1.17(ii), §1.17(ii), §1.17(i), §1.17(i), §1.17(iv), §1.18(ix), §1.18(iii), §1.18(vi), §1.18(i), §1.18(x).

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BibTeX

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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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ISSN 0029-599X, Document, FullText, MathReview (Mehdi Hassani), ZentralBlatt

Referenced by:

§19.36(iv), §19.36(iv).

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BibTeX

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4: Bibliography

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Tables of $\ln \mathrm{\Gamma }(z)$ for Complex Argument. Pergamon Press, New York.

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External Links:

ZentralBlatt

Referenced by:

§5.22(iii).

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BibTeX

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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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External Links:

ISSN 0373-1243, MathReview, ZentralBlatt

Referenced by:

§13.29(iii).

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BibTeX

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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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External Links:

FullText

Referenced by:

1st item, B. Döring (1966).

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BibTeX

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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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Notes:

Single and double precision, maximum accuracy 18S.

External Links:

ISSN 0098-3500, Document, Remark #1. Remark #2. GAMS (module 644; package TOMS), MathReview Entry, ZentralBlatt

Referenced by:

1st item, 1st item, 2nd item, 1st item.

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BibTeX

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Arb: A C Library for Arbitrary Precision Ball Arithmetic.

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Notes:

An extended-precision C code for special functions. The library uses arbitrary-precision ball arithmetic. Ball arithmetic is an efficient technique for performing numerical computations with automatic and rigorous tracking of error bounds. Arb is designed with computer algebra and computational number theory in mind, extending the principles behind FLINT to the domain of real and complex numbers.

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§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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5: Bibliography L

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Recurrence relations for hypergeometric functions of unit argument. Math. Comp. 45 (172), pp. 521–535.

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External Links:

ISSN 0025-5718, FullText, MathReview (S. Conde), ZentralBlatt

Referenced by:

§16.4(iii).

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Corrigenda: “Recurrence relations for hypergeometric functions of unit argument” [Math. Comp. 45 (1985), no. 172, 521–535; MR 86m:33004]. Math. Comp. 48 (178), pp. 853.

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External Links:

ISSN 0025-5718, FullText, MathReview, ZentralBlatt

Referenced by:

§16.4(iii).

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BibTeX

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Computations of spheroidal harmonics with complex arguments: A review with an algorithm. Phys. Rev. E 58 (5), pp. 6792–6806.

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Notes:

Mathematica package for eigenvalues and solutions of the spheroidal wave equations

External Links:

Code(SpheroidF), Document

Referenced by:

2nd item, 3rd item.

Encodings:

BibTeX

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On Bessel functions of equal order and argument. Rend. Sem. Mat. Univ. Politec. Torino 50 (2), pp. 209–216 (1993).

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External Links:

ISSN 0373-1243, MathReview (N. Hayek Calil), ZentralBlatt

Referenced by:

§10.14.

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BibTeX

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The Principle of Relativity: A Collection of Original Memoirs on the Special and General Theory of Relativity. Methuen and Co., Ltd., London.

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Notes:

Translated from Das Relativitätsprinzip by W. Perrett and G. B. Jeffery. Reprinted by Dover Publications Inc., New York, 1952.

External Links:

MathReview, ZentralBlatt

Referenced by:

§1.6(ii).

Encodings:

BibTeX

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6: Bibliography S

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Parabolic cylinder functions of integer and half-integer orders for nonnegative arguments. Comput. Phys. Comm. 115 (1), pp. 69–86.

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Notes:

Double-precision Fortran, minimum accuracy 14S, maximum accuracy 18D.

External Links:

ISSN 0010-4655, Document, Code, MathReview, ZentralBlatt

Referenced by:

3rd item.

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BibTeX

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Principles of Atomic Spectra. John Wiley & Sons Ltd., New York.

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External Links:

ISBN 0-471-78835-X

Referenced by:

§34.12.

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BibTeX

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Inequalities involving cylindrical functions of nearly equal argument and order. Proc. Amer. Math. Soc. 5 (3), pp. 337–344.

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External Links:

ISSN 0002-9939, FullText, MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

§10.14.

Encodings:

BibTeX

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An inequality involving Bessel functions of argument nearly equal to their order. Proc. Amer. Math. Soc. 4 (6), pp. 858–859.

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External Links:

ISSN 0002-9939, FullText, MathReview (N. D. Kazarinoff), ZentralBlatt

Referenced by:

§10.14.

Encodings:

BibTeX

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