Fourier cosine and sine transforms

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11: 28.2 Definitions and Basic Properties

… ►With $\zeta ={\sin }^{2}z$ we obtain the algebraic form of Mathieu’s equation …With $\zeta =\cos z$ we obtain another algebraic form: … ►The following three transformations … ► $\cos \left(\pi \nu \right)$ is an entire function of $a,q^2$. … ►The Fourier series of a Floquet solution …

12: Bibliography S

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Numerical evaluation of spherical Bessel transforms via fast Fourier transforms. J. Comput. Phys. 100 (2), pp. 294–296.

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External Links:

ISSN 0021-9991, Document, MathReview, ZentralBlatt

Referenced by:

§10.74(vii).

Encodings:

BibTeX

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Complements to asymptotic development of sine cosine integrals, and auxiliary functions. Univ. Beograd. Publ. Elecktrotehn. Fak., Ser. Mat. Fiz. 461–497, pp. 185–191.

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External Links:

MathReview (E. Riekstins), ZentralBlatt

Referenced by:

§6.15, §6.15.

Encodings:

BibTeX

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Automatic computing methods for special functions. III. The sine, cosine, exponential integrals, and related functions. J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 291–311.

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Notes:

Includes Fortran code, maximum accuracy 18S.

External Links:

MathReview (Martin E. Price), ZentralBlatt

Referenced by:

§6.21(ii).

Encodings:

BibTeX

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A Guide to Distribution Theory and Fourier Transforms. Studies in Advanced Mathematics, CRC Press, Boca Raton, FL.

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External Links:

ISBN 0-8493-8273-4, MathReview (J. Horváth), ZentralBlatt

Referenced by:

§18.17(v).

Encodings:

BibTeX

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An Introduction to Basic Fourier Series. Developments in Mathematics, Vol. 9, Kluwer Academic Publishers, Dordrecht.

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External Links:

ISBN 1-4020-1221-7, MathReview (P. D. F. Ion), ZentralBlatt

Referenced by:

§17.3(i).

Encodings:

BibTeX

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13: 22.20 Methods of Computation

… ►and the inverse sine has its principal value (§4.23(ii)). … ►

$\mathrm{cn}(x,k)=\cos {\varphi }_0,$

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§22.20(iii) Landen Transformations

►By application of the transformations given in §§22.7(i) and 22.7(ii), $k$ or $k^{\prime }$ can always be made sufficently small to enable the approximations given in §22.10(ii) to be applied. … ► $\mathrm{am}(x,k)$ can be computed from its definition (22.16.1) or from its Fourier series (22.16.9). …