modified%20expansions%20in%20terms%20of%20elementary%20functions

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1: 12.10 Uniform Asymptotic Expansions for Large Parameter

… ►With the upper sign in (12.10.2), expansions can be constructed for large

\mu

in terms of elementary functions that are uniform for

t\in(-\infty,\infty)

(§2.8(ii)). … ►The turning points can be included if expansions in terms of Airy functions are used instead of elementary functions (§2.8(iii)). … ►

§12.10(ii) Negative $a$ , $2\sqrt{-a}<x<\infty$

… ►

§12.10(vi) Modifications of Expansions in Elementary Functions

… ►

Modified Expansions

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2: Bibliography G

… ►

R. E. Gaunt (2014) Inequalities for modified Bessel functions and their integrals. J. Math. Anal. Appl. 420 (1), pp. 373–386.

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External Links:: ISSN 0022-247X, Document, Link, MathReview (Nihat Yagmur), ZentralBlatt
Referenced by:: §10.37, §10.37.
Encodings:: BibTeX

… ►

W. Gautschi (1959b) Some elementary inequalities relating to the gamma and incomplete gamma function. J. Math. Phys. 38 (1), pp. 77–81.

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External Links:: MathReview (H. O. Pollak), ZentralBlatt
Referenced by:: §5.6(i), §6.8, §7.8, §8.10.
Encodings:: BibTeX

… ►

A. Gil, J. Segura, and N. M. Temme (2003a) Computation of the modified Bessel function of the third kind of imaginary orders: Uniform Airy-type asymptotic expansion. J. Comput. Appl. Math. 153 (1-2), pp. 225–234.

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External Links:: ISSN 0377-0427, Document, MathReview, ZentralBlatt
Referenced by:: §10.45, §10.74(viii).
Encodings:: BibTeX

… ►

A. Gil, J. Segura, and N. M. Temme (2014) Algorithm 939: computation of the Marcum Q-function. ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.

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Notes:: Includes Fortran program claiming 12S accuracy
External Links:: ISSN 0098-3500, Link, Document, MathReview Entry, ZentralBlatt
Referenced by:: 3rd item, §10.77(ix).
Encodings:: BibTeX

… ►

GSL (free C library) GNU Scientific Library The GNU Project.

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Notes:: The GNU Scientific Library is a large general purpose numerical software library with broad coverage of elementary and special functions. Implementation is in double precision.
External Links:: Home Page
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.
Encodings:: BibTeX

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3: Bibliography C

… ►

A. Cayley (1895) An Elementary Treatise on Elliptic Functions. George Bell and Sons, London.

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Notes:: Republished by Dover Publications, Inc,, New York, 1961. Table erratum: Math. Comp. v. 29 (1975), no. 130, p. 670.
External Links:: ZentralBlatt
Referenced by:: §19.12, Ch.19, A. Cayley (1961).
Encodings:: BibTeX

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A. Cayley (1961) An Elementary Treatise on Elliptic Functions. Dover Publications, New York (English).

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Notes:: Second edition of Cayley (1895), unabridged and corrected
External Links:: ZentralBlatt
Referenced by:: §19.11(i), Erratum (V1.0.24) for Subsection 19.11(i).
Encodings:: BibTeX

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T. M. Cherry (1948) Expansions in terms of parabolic cylinder functions. Proc. Edinburgh Math. Soc. (2) 8, pp. 50–65.

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External Links:: MathReview (I. I. Hirschman, Jr.), ZentralBlatt
Referenced by:: §12.16.
Encodings:: BibTeX

… ►

W. J. Cody and W. Waite (1980) Software Manual for the Elementary Functions. Prentice-Hall, Englewood Cliffs.

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External Links:: ISBN 0138220646, ZentralBlatt
Referenced by:: §4.45(i).
Encodings:: BibTeX

… ►

W. J. Cody (1993a) Algorithm 714: CELEFUNT – A portable test package for complex elementary functions. ACM Trans. Math. Software 19 (1), pp. 1–21.

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External Links:: ISSN 0098-3500, Document, GAMS (module 714; package TOMS), ZentralBlatt
Referenced by:: 1st item.
Encodings:: BibTeX

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4: Bibliography M

… ►

T. M. MacRobert (1967) Spherical Harmonics. An Elementary Treatise on Harmonic Functions with Applications. 3rd edition, International Series of Monographs in Pure and Applied Mathematics, Vol. 98, Pergamon Press, Oxford.

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External Links:: MathReview (A. Erdélyi), ZentralBlatt
Referenced by:: Ch.14.
Encodings:: BibTeX

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Fr. Mechel (1966) Calculation of the modified Bessel functions of the second kind with complex argument. Math. Comp. 20 (95), pp. 407–412.

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External Links:: ISSN 0025-5718, FullText, MathReview (H. E. Fettis), ZentralBlatt
Referenced by:: §10.74(iii).
Encodings:: BibTeX

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X. Merrheim (1994) The computation of elementary functions in radix

2^{p}

. Computing 53 (3-4), pp. 219–232.

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Notes:: International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics (Vienna, 1993)
External Links:: ISSN 0010-485X, Document, MathReview, ZentralBlatt
Referenced by:: §4.45(i).
Encodings:: BibTeX

… ►

H. J. W. Müller (1966b) Asymptotic expansions of ellipsoidal wave functions in terms of Hermite functions. Math. Nachr. 32, pp. 49–62.

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External Links:: Document, MathReview (M. J. O. Strutt), ZentralBlatt
Referenced by:: §29.11, §29.7(ii).
Encodings:: BibTeX

… ►

J. Muller (1997) Elementary Functions: Algorithms and Implementation. Birkhäuser Boston Inc., Boston, MA.

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Notes:: A 2nd edition was published in 2006.
External Links:: ISBN 0-8176-3990-X, MathReview (Warren E. Ferguson, Jr.), ZentralBlatt
Referenced by:: §4.45(i).
Encodings:: BibTeX

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