divergence
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11: 2.11 Remainder Terms; Stokes Phenomenon
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►For divergent expansions the situation is even more difficult.
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►However, regardless whether we can bound the remainder, the accuracy achievable by direct numerical summation of a divergent asymptotic series is always limited.
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►The transformations in §3.9 for summing slowly convergent series can also be very effective when applied to divergent asymptotic series.
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12: 35.8 Generalized Hypergeometric Functions of Matrix Argument
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►If , then (35.8.1) converges absolutely for and diverges for .
►If , then (35.8.1) diverges unless it terminates.
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13: Bibliography F
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Studies on Divergent Series and Summability & The Asymptotic Developments of Functions Defined by Maclaurin Series.
Chelsea Publishing Co., New York.
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14: Bibliography H
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Divergent Series.
Clarendon Press, Oxford.
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15: 15.2 Definitions and Analytical Properties
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(c)
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Diverges when .
16: 31.11 Expansions in Series of Hypergeometric Functions
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►Such series diverge for Fuchs–Frobenius solutions.
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17: 2.7 Differential Equations
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►Hence unless the series (2.7.8) terminate (in which case the corresponding is zero) they diverge.
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►We cannot take and because would diverge as .
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18: 2.1 Definitions and Elementary Properties
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►Let be a formal power series (convergent or divergent) and for each positive integer ,
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19: 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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