confluent hypergeometric functions
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31—40 of 95 matching pages
31: 33.14 Definitions and Basic Properties
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§33.14(ii) Regular Solution
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33.14.4
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33.14.5
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►For nonzero values of and the function
is defined by
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33.14.7
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32: 13.21 Uniform Asymptotic Approximations for Large
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13.21.1
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13.21.6
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13.21.15
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13.21.16
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►For a uniform asymptotic expansion in terms of Airy functions for when is large and positive, is real with bounded, and see Olver (1997b, Chapter 11, Ex. 7.3).
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33: 13.13 Addition and Multiplication Theorems
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§13.13(i) Addition Theorems for
►The function has the following expansions: … ►The function has the following expansions: … ►
13.13.10
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§13.13(iii) Multiplication Theorems for and
…34: 13.24 Series
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►For expansions of arbitrary functions in series of
functions see Schäfke (1961b).
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13.24.1
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13.24.2
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35: 18.34 Bessel Polynomials
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§18.34(i) Definitions and Recurrence Relation
►For the confluent hypergeometric function and the generalized hypergeometric function , the Laguerre polynomial and the Whittaker function see §16.2(ii), §16.2(iv), (18.5.12), and (13.14.3), respectively. ►
18.34.1
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18.34.7_1
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36: 12.7 Relations to Other Functions
37: 7.18 Repeated Integrals of the Complementary Error Function
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Confluent Hypergeometric Functions
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7.18.9
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7.18.10
►The confluent hypergeometric function on the right-hand side of (7.18.10) is multivalued and in the sectors one has to use the analytic continuation formula (13.2.12).
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38: 13.15 Recurrence Relations and Derivatives
39: 9.6 Relations to Other Functions
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§9.6(iii) Airy Functions as Confluent Hypergeometric Functions
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9.6.21
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9.6.22
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9.6.23
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9.6.26
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40: 13.12 Products
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13.12.1
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