asymptotic%20expansions%20for%20large%20order
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11—13 of 13 matching pages
11: Bibliography P
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Error bounds for the uniform asymptotic expansion of the incomplete gamma function.
J. Comput. Appl. Math. 147 (1), pp. 215–231.
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A uniform asymptotic expansion for the incomplete gamma function.
J. Comput. Appl. Math. 148 (2), pp. 323–339.
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The asymptotic expansion of a generalised incomplete gamma function.
J. Comput. Appl. Math. 151 (2), pp. 297–306.
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Exactification of the method of steepest descents: The Bessel functions of large order and argument.
Proc. Roy. Soc. London Ser. A 460, pp. 2737–2759.
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Automatic computation of Bessel function integrals.
Comput. Phys. Comm. 25 (3), pp. 289–295.
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12: 9.9 Zeros
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►They are denoted by , , , , respectively, arranged in ascending order of absolute value for
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►They lie in the sectors and , and are denoted by , , respectively, in the former sector, and by , , in the conjugate sector, again arranged in ascending order of absolute value (modulus) for See §9.3(ii) for visualizations.
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§9.9(iv) Asymptotic Expansions
►For large … ►For error bounds for the asymptotic expansions of , , , and see Pittaluga and Sacripante (1991), and a conjecture given in Fabijonas and Olver (1999). …13: Bibliography K
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Asymptotic expansions of certain -series and a formula of Ramanujan for specific values of the Riemann zeta function.
Acta Arith. 107 (3), pp. 269–298.
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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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The asymptotic expansion of a hypergeometric function
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Math. Comp. 26 (120), pp. 963.
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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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Approximation Formulae for Generalized Hypergeometric Functions for Large Values of the Parameters.
J. B. Wolters, Groningen.
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