argument%20a%20fraction
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6 matching pages ♦
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6 matching pages
1: Bibliography K
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Series expansions for the third incomplete elliptic integral via partial fraction decompositions.
J. Comput. Appl. Math. 207 (2), pp. 331–337.
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Connection formulae for asymptotics of solutions of the degenerate third Painlevé equation. I.
Inverse Problems 20 (4), pp. 1165–1206.
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Algorithm 877: A subroutine package for cylindrical functions of complex order and nonnegative argument.
ACM Trans. Math. Software 34 (4), pp. Art. 22, 21.
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Algorithm 912: a module for calculating cylindrical functions of complex order and complex argument.
ACM Trans. Math. Software 37 (4), pp. Art. 47, 25.
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2: Bibliography M
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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An Introduction to the Fractional Calculus and Fractional Differential Equations.
A Wiley-Interscience Publication, John Wiley & Sons, Inc., New York.
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The dilogarithm function of a real argument.
Math. Comp. 33 (146), pp. 778–787.
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A new Stirling series as continued fraction.
Numer. Algorithms 56 (1), pp. 17–26.
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A continued fraction approximation of the gamma function.
J. Math. Anal. Appl. 402 (2), pp. 405–410.
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3: 20.11 Generalizations and Analogs
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►It is a discrete analog of theta functions.
If both are positive, then allows inversion of its arguments as a modular transformation (compare (23.15.3) and (23.15.4)):
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►Ramanujan’s theta function is defined by
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►In the case identities for theta functions become identities in the complex variable , with , that involve rational functions, power series, and continued fractions; see Adiga et al. (1985), McKean and Moll (1999, pp. 156–158), and Andrews et al. (1988, §10.7).
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►A further development on the lines of Neville’s notation (§20.1) is as follows.
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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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Some integrals involving three Bessel functions when their arguments satisfy the triangle inequalities.
J. Math. Phys. 25 (11), pp. 3350–3356.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Algorithm 490: The Dilogarithm function of a real argument [S22].
Comm. ACM 18 (4), pp. 200–202.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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5: Bibliography R
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A code to calculate (high order) Bessel functions based on the continued fractions method.
Comput. Phys. Comm. 76 (3), pp. 381–388.
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Computation of Hankel (Bessel) functions of complex index and argument by numerical integration of a Schläfli contour integral.
Ž. Vyčisl. Mat. i Mat. Fiz. 13, pp. 1415–1424, 1636.
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Mathieu functions of integral orders and real arguments.
IEEE Trans. Microwave Theory Tech. 28 (3), pp. 276–277.
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Total positivity properties of generalized hypergeometric functions of matrix argument.
J. Statist. Phys. 116 (1-4), pp. 907–922.
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Partial fractions expansions and identities for products of Bessel functions.
J. Math. Phys. 46 (4), pp. 043509–1–043509–18.
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6: Bibliography W
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A drop of water becomes a gateway into the world of catastrophe optics.
Scientific American 261, pp. 120–123.
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Analytic Theory of Continued Fractions.
D. Van Nostrand Company, Inc., New York.
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Asymptotic expansions of some matrix argument hypergeometric functions, with applications to macromolecules.
Ann. Inst. Statist. Math. 45 (3), pp. 467–475.
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Wave functions for large arguments by the amplitude-phase method.
Phys. Rev. 52, pp. 1123–1127.
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