transcendental functions

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1: Bibliography E

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Higher Transcendental Functions. Vol. I. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 65 (1996), no. 215, p. 1385, v. 41 (1983), no. 164, p. 778, v. 30 (1976), no. 135, p. 675, v. 25 (1971), no. 115, p. 635, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 112, p. 999, v. 24 (1970), no. 110, p. 504, v. 17 (1963), no. 84, p. 485.

External Links:

MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§13.1, §13.10(ii), §13.10(iv), §13.12, §13.13(i), §13.16(ii), §13.16(iii), §13.23(i), §13.23(ii), §13.25, §13.4(i), §13.4(ii), §13.9(i), §13.9(ii), Ch.13, §14.1, §14.10, §14.12(ii), §14.12(i), §14.12(ii), §14.13, §14.13, §14.17(ii), §14.17(iv), §14.18(ii), §14.18(iii), §14.18(iv), §14.19(i), §14.19(ii), §14.19(iii), §14.19(iv), §14.20(v), §14.21(iii), §14.25, §14.28(i), §14.28(ii), §14.3(iii), §14.3(iii), §14.3(iv), §14.5(iii), §14.5(iv), §14.6(i), §14.6(ii), §14.7(iv), §14.8(i), §14.8(ii), Ch.14, §15.16, §15.4(iii), §15.5(i), §15.6, §15.8(v), §15.8(ii), §15.8(v), §15.9(iii), Ch.15, §16.12, §16.12, §16.13, §16.14(i), §16.14(ii), (16.15.3), §16.15, §16.16(i), §16.16(ii), §16.18, §16.20, §16.20, §16.21, §16.4(ii), §16.5, §16.6, Ch.16, §19.21(i), §19.28, §19.5, §24.16(iii), §24.5(i), §24.7(i), §24.7(ii), §24.8(i), Ch.24, (25.11.12), (25.11.18), (25.11.29), (25.11.30), (25.12.12), (25.12.13), (25.14.1), (25.14.4), (25.14.5), (25.14.6), §25.14(i), §25.14(i), §25.14(ii), §25.14(ii), §25.14, (25.5.1), (25.5.10), (25.5.11), (25.5.20), (25.5.21), (25.5.3), (25.5.8), (25.5.9), §25.5(i), §25.5(iii), §25.5, (25.8.5), (25.8.6), §25.8, Ch.25, §5.7(i), Ch.5, Notations P, Notations P, Notations Q.

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Higher Transcendental Functions. Vol. II. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 41 (1983), no. 164, p. 778, v. 36 (1981), no. 153, p. 315, v. 30 (1976), no. 135, p. 675, v. 29 (1975), no. 130, p. 670, v. 26 (1972), no. 118, p. 598, v. 25 (1971), no. 113, p. 199, v. 24 (1970), no. 109, p. 239, v. 17 (1963), no. 84, p. 485.

External Links:

MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§10.22(iv), §10.22(vi), §10.23(iii), §10.23(iii), §10.23(iv), §10.32(i), §10.32(iii), §10.32(iv), §10.43(iv), §10.43(vi), §10.44(iv), §10.60(iv), §10.9(i), §10.9(iii), §10.9(iv), §11.10(vi), §11.4(i), Ch.11, §12.12, §12.12, §12.13(i), §12.5(iv), Ch.12, §18.16(vi), (18.17.21_1), §18.17(iv), §18.17(i), §18.17(viii), (18.35.1), (18.35.2), (18.35.4_5), §18.35(i), (18.5.11_1), (18.5.11_3), §18.5(ii), §18.9(iii), §19.1, §19.10(i), §19.14(ii), (19.25.40), §19.25(vi), §19.5, §19.7(ii), §19.9(i), Ch.19, §20.9(i), §22.15(ii), §23.6(iv), Ch.23, §8.13(i), §8.14, §8.3(i), §8.4, §8.6(iii), §8.7, Ch.8, Notations P, Notations P.

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Higher Transcendental Functions. Vol. III. McGraw-Hill Book Company, Inc., New York-Toronto-London.

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Notes:

Reprinted by Robert E. Krieger Publishing Co. Inc., 1981. Table errata: Math. Comp. v. 41 (1983), no. 164, p. 778.

External Links:

MathReview (E. T. Copson), ZentralBlatt

Referenced by:

§10.46, §27.2(i), Ch.27, Table 28.1.1, §28.10(iii), §28.2(iii), §28.2(v), §29.1, §29.10, §29.11, §29.14, §29.17(i), §29.17(iii), §29.18(i), §29.18(ii), §29.18(iii), §29.18(iii), §29.2(i), §29.2(ii), §29.3(i), §29.3(ii), §29.3(ii), §29.3(iv), §29.5, §29.6(i), §29.6(ii), §29.6(iii), §29.6(iv), §29.8, §29.8, Ch.29, §30.1, §30.10, §30.11(v), §30.11(vi), §30.13(i), §30.14(i), §30.9(iii), Ch.30, §31.2(i), §31.4, §31.5, Ch.31.

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2: 32.2 Differential Equations

… ►For arbitrary values of the parameters $\alpha$, $\beta$, $\gamma$, and $\delta$, the general solutions of ${\text{P}}_{\text{I}}$–${\text{P}}_{\text{VI}}$ are transcendental, that is, they cannot be expressed in closed-form elementary functions. …

3: Bibliography M

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Handbook of Integral Transforms of Higher Transcendental Functions: Theory and Algorithmic Tables. Ellis Horwood Ltd./John Wiley & Sons, Inc, Chichester/New York.

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Notes:

Edited by F. D. Gakhov, Translated from the Russian by L. W. Longdon

External Links:

ISBN 0-85312-538-7, MathReview, ZentralBlatt

Referenced by:

§1.14(viii), §10.22(vi), §10.32(iv), §10.43(vi), §10.9(iv), §11.10(x), §11.7(v), §11.9(iv), §12.12, §13.10(iii), §13.23(i), §14.17(vi), §15.14, §18.17(ix), §6.14(iii), §7.14(iii), §8.14.

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Nested sums, expansion of transcendental functions, and multiscale multiloop integrals. J. Math. Phys. 43 (6), pp. 3363–3386.

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External Links:

ISSN 0022-2488, Document, MathReview (Driss Essouabri), ZentralBlatt

Referenced by:

§16.24(ii).

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Notes:

Mpmath is a pure-Python library for multiprecision floating-point arithmetic. It provides an extensive set of transcendental functions, unlimited exponent sizes, complex numbers, interval arithmetic, numerical integration and differentiation, root-finding, linear algebra, and much more.

External Links:

mpmath

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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4: Bibliography G

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A continued fraction algorithm for the computation of higher transcendental functions in the complex plane. Math. Comp. 21 (97), pp. 18–29.

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External Links:

FullText, MathReview (D. C. Gilles), ZentralBlatt

Referenced by:

§10.74(v), §3.10(ii).

Encodings:

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5: 32.10 Special Function Solutions

… ►The solution (32.10.34) is an essentially transcendental function of both constants of integration since ${\text{P}}_{\text{VI}}$ with $\alpha =\beta =\gamma =0$ and $\delta =\frac{1}{2}$ does not admit an algebraic first integral of the form $P(z,w,w^{\prime },C)=0$, with $C$ a constant. …

6: Bibliography P

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Notes:

Computer algebra system designed for computations in number theory. Many transcendental functions are also included. PARI is also available as a C library to allow for faster computations. Originally developed by Henri Cohen and co-workers at the Université Bordeaux I.

External Links:

Home Page

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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7: Bibliography B

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Transcendental Functions Satisfying Nonhomogeneous Linear Differential Equations. The Macmillan Co., New York.

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External Links:

MathReview (H. Hochstadt), ZentralBlatt

Referenced by:

§11.4(i), §11.4(v), §11.5(ii), §11.5(i), §11.5(ii), §11.5(iii), §11.7(ii), §11.7(iii), §11.7(v), §11.9(i), §11.9(iv), §11.9(iv), Ch.11, §14.29.

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8: Bibliography C

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Notes:

This library treats about 180 different mathematical functions, including a substantial collection of probability integrals, Bessel functions, and higher transcendental functions. Implementations in single, double, and quad precisions are provided. See Moshier (1989).

External Links:

GAMS (package CEPHES)

Referenced by:

§ ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index, § ‣ Software Cross Index.

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9: 2.2 Transcendental Equations

§2.2 Transcendental Equations

►Let $f(x)$ be continuous and strictly increasing when and … ►An important case is the reversion of asymptotic expansions for zeros of special functions. …where $F_0=f_0$ and $s{F}_s$ ($s\ge 1$) is the coefficient of $x^{-1}$ in the asymptotic expansion of ${(f(x))}^s$ (Lagrange’s formula for the reversion of series). …Applications to real and complex zeros of Airy functions are given in Fabijonas and Olver (1999). …

10: Bibliography F

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Generalized parabolic cylinder functions. Asymptotic Anal. 5 (6), pp. 517–531.

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External Links:

ISSN 0921-7134, MathReview (Wolfgang Bühring), ZentralBlatt

Referenced by:

§12.15.

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Complex zeros of the error function and of the complementary error function. Math. Comp. 27 (122), pp. 401–407.

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External Links:

FullText, MathReview, ZentralBlatt

Referenced by:

§7.13(i), §7.13(ii), 1st item.

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Expansions of hypergeometric functions in hypergeometric functions. Math. Comp. 15 (76), pp. 390–395.

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External Links:

FullText, MathReview (L. J. Slater), ZentralBlatt

Referenced by:

§16.10.

Encodings:

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Spheroidal Wave Functions. Stanford University Press, Stanford, CA.

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External Links:

MathReview (J. C. P. Miller), ZentralBlatt

Referenced by:

§30.1, §30.10, 2nd item, Ch.30.

Encodings:

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Solution of the transcendental equation $w{e}^w=x$ . Comm. ACM 16 (2), pp. 123–124.

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Notes:

Includes Fortran code.

External Links:

ISSN 0001-0782, Document

Referenced by:

§4.48(iv).

Encodings:

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