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1—10 of 874 matching pages

1: Bibliography T

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J. D. Talman (1983) LSFBTR: A subroutine for calculating spherical Bessel transforms. Comput. Phys. Comm. 30 (1), pp. 93–99.

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Notes:: Single-precision Fortran.
External Links:: ISSN 0010-4655, Document, Code
Referenced by:: 9th item.
Encodings:: BibTeX

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P. G. Todorov (1978) Une nouvelle représentation explicite des nombres d’Euler. C. R. Acad. Sci. Paris Sér. A-B 286 (19), pp. A807–A809.

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External Links:: MathReview, ZentralBlatt
Referenced by:: §24.6.
Encodings:: BibTeX

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A. Trellakis, A. T. Galick, and U. Ravaioli (1997) Rational Chebyshev approximation for the Fermi-Dirac integral

F_{-3/2}(x)

. Solid–State Electronics 41 (5), pp. 771–773.

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External Links:: Document
Referenced by:: §25.21(vii).
Encodings:: BibTeX

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M. J. Tretter and G. W. Walster (1980) Further comments on the computation of modified Bessel function ratios. Math. Comp. 35 (151), pp. 937–939.

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External Links:: ISSN 0025-5718, FullText, Document, MathReview (James M. Horner), ZentralBlatt
Referenced by:: §10.74(v).
Encodings:: BibTeX

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F. G. Tricomi (1949) Sul comportamento asintotico dell’

n

-esimo polinomio di Laguerre nell’intorno dell’ascissa

4n

. Comment. Math. Helv. 22, pp. 150–167.

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External Links:: ISSN 0010-2571, Document, MathReview (G. Szegő), ZentralBlatt
Referenced by:: §18.16(iv).
Encodings:: BibTeX

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2: 6 Exponential, Logarithmic, Sine, and
Cosine Integrals

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3: 7 Error Functions, Dawson’s and Fresnel Integrals

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4: 7.24 Approximations

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Cody (1968) gives minimax rational approximations for the Fresnel integrals (maximum relative precision 19S); for a Fortran algorithm and comments see Snyder (1993).

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Luke (1969b, pp. 323–324) covers $\frac{1}{2}\sqrt{\pi}\operatorname{erf}x$ and $e^{x^{2}}F\left(x\right)$ for $-3\leq x\leq 3$ (the Chebyshev coefficients are given to 20D); $\sqrt{\pi}xe^{x^{2}}\operatorname{erfc}x$ and $2xF\left(x\right)$ for $x\geq 3$ (the Chebyshev coefficients are given to 20D and 15D, respectively). Coefficients for the Fresnel integrals are given on pp. 328–330 (20D).

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Schonfelder (1978) gives coefficients of Chebyshev expansions for $x^{-1}\operatorname{erf}x$ on $0\leq x\leq 2$ , for $xe^{x^{2}}\operatorname{erfc}x$ on $[2,\infty)$ , and for $e^{x^{2}}\operatorname{erfc}x$ on $[0,\infty)$ (30D).

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5: Bibliography K

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D. A. Kofke (2004) Comment on “The incomplete beta function law for parallel tempering sampling of classical canonical systems” [J. Chem. Phys. 120, 4119 (2004)]. J. Chem. Phys. 121 (2), pp. 1167.

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External Links:: Document
Referenced by:: §8.24(ii).
Encodings:: BibTeX

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K. S. Kölbig (1981) A Program for Computing the Conical Functions of the First Kind

P^{m}_{-1/2+i\tau}(x)

for

m=0

and

m=1

. Comput. Phys. Comm. 23 (1), pp. 51–61.

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Notes:: Single-precision Fortran, maximum accuracy 15D.
External Links:: Document, Code
Referenced by:: §14.31(ii), 1st item.
Encodings:: BibTeX

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S. Kowalevski (1889) Sur le problème de la rotation d’un corps solide autour d’un point fixe. Acta Math. 12 (1), pp. 177–232 (French).

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External Links:: ISSN 0001-5962, Document, MathReview Entry, ZentralBlatt
Referenced by:: §22.19(iv).
Encodings:: BibTeX

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C. Krattenthaler (1993) HYP and HYPQ. Mathematica packages for the manipulation of binomial sums and hypergeometric series respectively

q

-binomial sums and basic hypergeometric series. Séminaire Lotharingien de Combinatoire 30, pp. 61–76.

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Notes:: Also published in J. Symbolic Comput. (1995), v. 20, no. 5–6, pp. 737–744.
External Links:: Code, Document, MathReview (G. Gasper), ZentralBlatt
Referenced by:: 1st item.
Encodings:: BibTeX

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M. D. Kruskal (1974) The Korteweg-de Vries Equation and Related Evolution Equations. In Nonlinear Wave Motion (Proc. AMS-SIAM Summer Sem., Clarkson Coll. Tech., Potsdam, N.Y., 1972), A. C. Newell (Ed.), Lectures in Appl. Math., Vol. 15, pp. 61–83.

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External Links:: MathReview (G. L. Lamb, Jr.), ZentralBlatt
Referenced by:: §22.19(iii).
Encodings:: BibTeX

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6: 27 Functions of Number Theory

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7: Bibliography S

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R. Sips (1949) Représentation asymptotique des fonctions de Mathieu et des fonctions d’onde sphéroidales. Trans. Amer. Math. Soc. 66 (1), pp. 93–134 (French).

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External Links:: FullText, MathReview (M. Strutt), ZentralBlatt
Referenced by:: §28.8(ii).
Encodings:: BibTeX

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R. Sips (1967) Répartition du courant alternatif dans un conducteur cylindrique de section elliptique. Acad. Roy. Belg. Bull. Cl. Sci. (5) 53 (8), pp. 861–878.

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Referenced by:: 6th item.
Encodings:: BibTeX

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I. Sh. Slavutskiĭ (1999) About von Staudt congruences for Bernoulli numbers. Comment. Math. Univ. St. Paul. 48 (2), pp. 137–144.

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External Links:: ISSN 0010-258X, MathReview (Arnold M. Adelberg), ZentralBlatt
Referenced by:: §24.10(ii).
Encodings:: BibTeX

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D. Slepian (1983) Some comments on Fourier analysis, uncertainty and modeling. SIAM Rev. 25 (3), pp. 379–393.

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External Links:: ISSN 0036-1445, Document, MathReview (H. Vincent Poor), ZentralBlatt
Referenced by:: §30.15(ii), §30.15(iii), §30.15(iv), §30.15(v), §30.15(v).
Encodings:: BibTeX

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O. Szász (1950) On the relative extrema of ultraspherical polynomials. Boll. Un. Mat. Ital. (3) 5, pp. 125–127.

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External Links:: MathReview (A. Erdélyi), ZentralBlatt
Referenced by:: §18.14(iii).
Encodings:: BibTeX

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8: Guide to Searching the DLMF

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Table 1: Query Examples

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Query	Matching records contain
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`1/(2pi) and "Fourier transform"`	both $1/(2\pi)$ and the phrase “Fourier transform”.
…

► … ►Be careful, however, because if you put quotes around math expressions involving math symbols, you may not get the matches you’d expect. … ►

Table 3: A sample of recognized symbols