am function

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11—20 of 29 matching pages

11: Diego Dominici

… ►Dominici published numerous papers in asymptotics and special functions and organized many meetings and conferences for events of the AMS, SIAM and the European Consortium on Mathematics in Industry. …

12: 22.14 Integrals

… ►

22.14.3

\int\operatorname{dn}\left(x,k\right)\,\mathrm{d}x=\operatorname{Arcsin}\left(% \operatorname{sn}\left(x,k\right)\right)=\operatorname{am}\left(x,k\right).

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Symbols:: $\operatorname{am}\left(\NVar{x},\NVar{k}\right)$ : Jacobi’s amplitude function, $\operatorname{dn}\left(\NVar{z},\NVar{k}\right)$ : Jacobian elliptic function, $\operatorname{sn}\left(\NVar{z},\NVar{k}\right)$ : Jacobian elliptic function, $\,\mathrm{d}\NVar{x}$ : differential of $x$ , $\int$ : integral, $\operatorname{Arcsin}\NVar{z}$ : general arcsine function, $x$ : real and $k$ : modulus
A&S Ref:: 16.24.3
Permalink:: http://dlmf.nist.gov/22.14.E3
Encodings:: pMML, png, TeX
See also:: Annotations for §22.14(i), §22.14 and Ch.22

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13: George E. Andrews

… ►Andrews served as President of the AMS from February 1, 2009 to January 31, 2011, and became a Fellow of the AMS in 2012. … ►

17 q-Hypergeometric and Related Functions

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14: 29.2 Differential Equations

… ►

29.2.5

\phi=\tfrac{1}{2}\pi-\operatorname{am}\left(z,k\right).

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Defines:: $\phi$ : change of variable (locally)
Symbols:: $\operatorname{am}\left(\NVar{x},\NVar{k}\right)$ : Jacobi’s amplitude function, $\pi$ : the ratio of the circumference of a circle to its diameter, $z$ : complex variable and $k$ : real parameter
Referenced by:: §29.15(i), §29.15(ii), §29.6(i)
Permalink:: http://dlmf.nist.gov/29.2.E5
Encodings:: pMML, png, TeX
See also:: Annotations for §29.2(ii), §29.2 and Ch.29

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15: 8.2 Definitions and Basic Properties

§8.2 Definitions and Basic Properties

… ►The general values of the incomplete gamma functions

\gamma\left(a,z\right)

and

\Gamma\left(a,z\right)

are defined by … ►Normalized functions are: … ►

§8.2(ii) Analytic Continuation

… ►

§8.2(iii) Differential Equations

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16: 29.1 Special Notation

… ►(For other notation see Notation for the Special Functions.) … ►All derivatives are denoted by differentials, not by primes. … ►The notation for the eigenvalues and functions is due to Erdélyi et al. (1955, §15.5.1) and that for the polynomials is due to Arscott (1964b, §9.3.2). … ►where

\psi=\operatorname{am}\left(z,k\right)

; see §22.16(i). The relation to the Lamé functions

{\rm Ec}^{m}_{\nu}

{\rm Es}^{m}_{\nu}

of Ince (1940b) is given by …

17: Richard A. Askey

… ►His well-known book Special Functions (with G. … ►Additional books for which Askey served as author or editor include Orthogonal Polynomials and Special Functions, published by SIAM in 1975, Theory and application of special functions, published by Academic Press in 1975, Special Functions: Group Theoretical Aspects and Applications (with T. … ►He was elected Fellow of the Society for Industrial and Applied Mathematics (SIAM) in 2009 and Fellow of the American Mathematical Society (AMS) in 2012. … ►

5 Gamma Function

►

16 Generalized Hypergeometric Functions & Meijer G-Function

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18: 29.6 Fourier Series

§29.6 Fourier Series

►

§29.6(i) Function $\mathit{Ec}^{2m}_{\nu}\left(z,k^{2}\right)$

►With

\phi=\frac{1}{2}\pi-\operatorname{am}\left(z,k\right)

, as in (29.2.5), we have … ►In addition, if

H

satisfies (29.6.2), then (29.6.3) applies. … ►

§29.6(ii) Function $\mathit{Ec}^{2m+1}_{\nu}\left(z,k^{2}\right)$

…

19: Need Help?

… ►In the Digital Library of Mathematical Functions, we have tried to provide the most accurate, carefully selected information about Special Functions possible. … ►

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What’s this ‘MathML’, anyway? See About MathML.

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20: Bibliography D

… ►

H. T. Davis (1933) Tables of Higher Mathematical Functions I. Principia Press, Bloomington, Indiana.

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External Links:: ZentralBlatt
Referenced by:: §5.1, Notations P.
Encodings:: BibTeX

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A. Dienstfrey and J. Huang (2006) Integral representations for elliptic functions. J. Math. Anal. Appl. 316 (1), pp. 142–160.

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External Links:: ISSN 0022-247X, Document, MathReview Entry, ZentralBlatt
Referenced by:: §23.11.
Encodings:: BibTeX

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P. G. L. Dirichlet (1837) Beweis des Satzes, dass jede unbegrenzte arithmetische Progression, deren erstes Glied und Differenz ganze Zahlen ohne gemeinschaftlichen Factor sind, unendlich viele Primzahlen enthält. Abhandlungen der Königlich Preussischen Akademie der Wissenschaften von 1837, pp. 45–81 (German).

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Notes:: Reprinted in G. Lejeune Dirichlet’s Werke, Band I, pp. 313–342, Reimer, Berlin, 1889 and with corrections in G. Lejeune Dirichlet’s Werke, AMS Chelsea Publishing Series, Providence, RI, 1969.
External Links:: ISBN 0-8284-0225-6, Link, MathReview
Referenced by:: §25.15(i).
Encodings:: BibTeX

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P. G. L. Dirichlet (1849) Über die Bestimmung der mittleren Werthe in der Zahlentheorie. Abhandlungen der Königlich Preussischen Akademie der Wissenschaften von 1849, pp. 69–83 (German).

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Notes:: Reprinted in G. Lejeune Dirichlet’s Werke, Band II, pp. 49–66, Reimer, Berlin, 1897 and with corrections in G. Lejeune Dirichlet’s Werke, AMS Chelsea Publishing Series, Providence, RI, 1969.
External Links:: ISBN 0-8284-0225-6, Link, MathReview
Referenced by:: §27.11.
Encodings:: BibTeX

… ►

A. J. Durán (1993) Functions with given moments and weight functions for orthogonal polynomials. Rocky Mountain J. Math. 23, pp. 87–104.

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External Links:: ISSN 0035-7596, MathReview (Olav Njåstad), ZentralBlatt
Referenced by:: §18.34(ii).
Encodings:: BibTeX

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