convergence%20properties
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1: 20.11 Generalizations and Analogs
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►For applications to rapidly convergent expansions for see Chudnovsky and Chudnovsky (1988), and for applications in the construction of elliptic-hypergeometric series see Rosengren (2004).
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►Multidimensional theta functions with characteristics are defined in §21.2(ii) and their properties are described in §§21.3(ii), 21.5(ii), and 21.6.
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2: 25.12 Polylogarithms
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§25.12(i) Dilogarithms
… ►For graphics see Figures 25.12.1 and 25.12.2, and for further properties see Maximon (2003), Kirillov (1995), Lewin (1981), Nielsen (1909), and Zagier (1989). … ►§25.12(ii) Polylogarithms
… ►The series also converges when , provided that . … ►Further properties include …3: 8.17 Incomplete Beta Functions
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§8.17(i) Definitions and Basic Properties
… ►The and convergents are less than , and the and convergents are greater than . … ►The expansion (8.17.22) converges rapidly for . For or , more rapid convergence is obtained by computing and using (8.17.4). … ►§8.17(vii) Addendum to 8.17(i) Definitions and Basic Properties
…4: 5.11 Asymptotic Expansions
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►The scaled gamma function is defined in (5.11.3) and its main property is as in the sector .
Wrench (1968) gives exact values of up to .
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►For similar results including a convergent factorial series see, Nemes (2013c).
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5: Bibliography S
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Non-linear transformations of divergent and slowly convergent sequences.
J. Math. Phys. 34, pp. 1–42.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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Some properties of polynomial sets of type zero.
Duke Math. J. 5, pp. 590–622.
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Staudt and arithmetical properties of Bernoulli numbers.
Historia Sci. (2) 5 (1), pp. 69–74.
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Some combinatorial properties of Jack symmetric functions.
Adv. Math. 77 (1), pp. 76–115.
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6: Bibliography N
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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The resurgence properties of the large order asymptotics of the Anger-Weber function I.
J. Class. Anal. 4 (1), pp. 1–39.
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The resurgence properties of the large order asymptotics of the Anger-Weber function II.
J. Class. Anal. 4 (2), pp. 121–147.
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The resurgence properties of the incomplete gamma function II.
Stud. Appl. Math. 135 (1), pp. 86–116.
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Bisection hardly ever converges linearly.
Numer. Math. 70 (1), pp. 111–118.
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