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11: 15.11 Riemann’s Differential Equation

… ►A conformal mapping of the extended complex plane onto itself has the form ►

15.11.5 $$t=(\kappa z+\lambda )/(\mu z+\nu ),$$

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Symbols:

$z$: complex variable, $t$: mapping, $\kappa$: constant, $\lambda$: constant, $\mu$: constant and $\nu$: constant

Permalink:

http://dlmf.nist.gov/15.11.E5

Encodings:

pMML, png, TeX

See also:

Annotations for §15.11(ii), §15.11 and Ch.15

… ►These constants can be chosen to map any two sets of three distinct points $\{\alpha ,\beta ,\gamma \}$ and $\{\tilde{\alpha },\tilde{\beta },\tilde{\gamma }\}$ onto each other. … ►

15.11.6

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Symbols:

: Riemann’s $P$-symbol for solutions of the generalized hypergeometric differential equation, $z$: complex variable, $a$: real or complex parameter, $b$: real or complex parameter, $c$: real or complex parameter, $\alpha$: point, $\beta$: point, $\gamma$: point and $t$: mapping

Permalink:

http://dlmf.nist.gov/15.11.E6

Encodings:

pMML, png, TeX

See also:

Annotations for §15.11(ii), §15.11 and Ch.15

…

12: Bibliography I

… ►

The real roots of Bernoulli polynomials. Ann. Univ. Turku. Ser. A I 37, pp. 1–20.

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External Links:

MathReview (D. H. Lehmer), ZentralBlatt

Referenced by:

§24.12(i).

Encodings:

BibTeX

… ►

Statistical Field Theory: Strong Coupling, Monte Carlo Methods, Conformal Field Theory, and Random Systems. Vol. 2, Cambridge University Press, Cambridge.

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External Links:

ISBN 0-521-37012-4; 0-521-40806-7, MathReview (C. A. Hurst), ZentralBlatt

Referenced by:

2nd item.

Encodings:

BibTeX

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13: 1.9 Calculus of a Complex Variable

… ►

§1.9(iv) Conformal Mapping

… ►

Conformal Transformation

… ►We then say that the mapping $w=f(z)$ is conformal (angle-preserving) at $z_0$. … ► … ►The transformation (1.9.40) is a one-to-one conformal mapping of $ℂ\cup \{\mathrm{\infty }\}$ onto itself. …

14: 15.18 Physical Applications

… ►More varied applications include photon scattering from atoms (Gavrila (1967)), energy distributions of particles in plasmas (Mace and Hellberg (1995)), conformal field theory of critical phenomena (Burkhardt and Xue (1991)), quantum chromo-dynamics (Atkinson and Johnson (1988)), and general parametrization of the effective potentials of interaction between atoms in diatomic molecules (Herrick and O’Connor (1998)).

15: Bibliography H

… ►

Applied and Computational Complex Analysis. Vol. 1: Power Series—Integration—Conformal Mapping—Location of Zeros. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons], New York.

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Notes:

Reprinted in 1988.

External Links:

ISBN 0-471-37244-7, MathReview (M. Marden), ZentralBlatt

Referenced by:

§1.10(vii), §1.9(vi), Ch.3.

Encodings:

BibTeX

… ►

Applied and Computational Complex Analysis. Vol. 3: Discrete Fourier Analysis—Cauchy Integrals—Construction of Conformal Maps—Univalent Functions. Pure and Applied Mathematics, Wiley-Interscience [John Wiley & Sons Inc.], New York.

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Notes:

Reprinted in 1993.

External Links:

ISBN 0-471-08703-3; 0-471-58986-1, MathReview (A. E. Heins), ZentralBlatt

Referenced by:

§1.14(v), Ch.3.

Encodings:

BibTeX

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16: 20 Theta Functions

Chapter 20 Theta Functions

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17: About Color Map

About Color Map

… ►

Height Mapping

… ►

Phase Mappings

… ►

Four Color Phase Mapping

… ►

Continuous Phase Mapping

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18: 4.37 Inverse Hyperbolic Functions

… ►This section also indicates conformal mappings, and surface plots for complex arguments. …

19: Bibliography B

… ►

Pionic atoms. Annual Review of Nuclear and Particle Science 20, pp. 467–508.

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External Links:

Document

Referenced by:

§33.22(iv).

Encodings:

BibTeX

… ►

A program for computing the Riemann zeta function for complex argument. Comput. Phys. Comm. 20 (3), pp. 441–445.

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Notes:

Double-precision Fortran, maximum accuracy 10S.

External Links:

Document, Code, ZentralBlatt

Referenced by:

1st item.

Encodings:

BibTeX

… ►

Coulomb functions (negative energies). Comput. Phys. Comm. 20 (3), pp. 447–458.

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Notes:

Double-precision Fortran code.

External Links:

Document, Code

Referenced by:

1st item, 4th item.

Encodings:

BibTeX

… ►

Some solutions of the problem of forced convection. Philos. Mag. Series 7 20, pp. 322–343.

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External Links:

Document, ZentralBlatt

Referenced by:

§10.73(iv).

Encodings:

BibTeX

… ►

Density profiles in confined critical systems and conformal invariance. Phys. Rev. Lett. 66 (7), pp. 895–898.

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External Links:

Document

Referenced by:

§15.18.

Encodings:

BibTeX

…

20: 26.13 Permutations: Cycle Notation

… ► $\sigma \in {𝔖}_n$ is a one-to-one and onto mapping from $\{1,2,\mathrm{\dots },n\}$ to itself. …