auxiliary functions for sine and cosine integrals

SearchAdvancedHelp

(0.007 seconds)

21—22 of 22 matching pages

21: 7.7 Integral Representations

§7.7 Integral Representations

►

§7.7(i) Error Functions and Dawson’s Integral

►Integrals of the type $\int {\mathrm{e}}^{-z^2}R(z)dz$, where $R(z)$ is an arbitrary rational function, can be written in closed form in terms of the error functions and elementary functions. … ►

§7.7(ii) Auxiliary Functions

… ►

Mellin–Barnes Integrals

…

22: Bibliography F

… ►

Tables of Values of the Function $w(z)=e^{-z^2}(1+2i{\pi }^{-1/2}{\int }_0^z{e}^{t^2}𝑑t)$ for Complex Argument. Edited by V. A. Fok; translated from the Russian by D. G. Fry. Mathematical Tables Series, Vol. 11, Pergamon Press, Oxford.

ⓘ

External Links:

MathReview, ZentralBlatt

Referenced by:

V. N. Faddeeva and N. M. Terent’ev (1954).

Encodings:

BibTeX

… ►

A Table of the Complete Elliptic Integral of the First Kind for Complex Values of the Modulus. Part I. Technical report Technical Report ARL 69-0172, Aerospace Research Laboratories, Office of Aerospace Research, Wright-Patterson Air Force Base, Ohio.

ⓘ

Notes:

Table erratum: Math. Comp. v. 36 (1981), no. 153, p. 318. Part II of this report, with the same date but numbered ARL 69-0173, again puts $k=R\exp (i\theta )$ but with $R$ as parameter and $\theta$ as variable instead of the other way around. Part III, dated May 1970 and numbered ARL 70-0081, contains tables of auxiliary functions to help interpolation.

External Links:

MathReview, ZentralBlatt

Referenced by:

§19.36(ii), §19.37(ii).

Encodings:

BibTeX

… ►

Complex roots of $\sin z=az$, $\cos z=az$, and $\cosh z=az$ . Math. Comp. 30 (135), pp. 541–545.

ⓘ

External Links:

FullText, MathReview (Gerhard Merz), ZentralBlatt

Referenced by:

§4.46.

Encodings:

BibTeX

… ►

Error bounds for a uniform asymptotic expansion of the Legendre function $Q_n^{-m}(\cosh z)$ . SIAM J. Math. Anal. 21 (2), pp. 523–535.

ⓘ

External Links:

ISSN 0036-1410, Document, MathReview (F. W. J. Olver), ZentralBlatt

Referenced by:

§14.26.

Encodings:

BibTeX

… ►

Characteristic values of the integral equation satisfied by the Mathieu functions and its application to a system with chirality-pair interaction on a one-dimensional lattice. Phys. A 190 (3-4), pp. 346–362.

ⓘ

External Links:

ISSN 0378-4371, Document, MathReview

Referenced by:

6th item.

Encodings:

BibTeX

…