Kummer functions
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11—20 of 64 matching pages
11: 13.8 Asymptotic Approximations for Large Parameters
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§13.8(i) Large , Fixed and
… ►§13.8(ii) Large and , Fixed and
… ►§13.8(iii) Large
… ► … ►§13.8(iv) Large and
…12: 13.9 Zeros
13: 13.11 Series
14: 13.7 Asymptotic Expansions for Large Argument
§13.7 Asymptotic Expansions for Large Argument
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13.7.1
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§13.7(ii) Error Bounds
… ►§13.7(iii) Exponentially-Improved Expansion
… ►For extensions to hyperasymptotic expansions see Olde Daalhuis and Olver (1995a).15: 13.28 Physical Applications
§13.28 Physical Applications
…16: Bibliography Y
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Computation of Kummer functions
for large argument by using the -method.
Trans. Inform. Process. Soc. Japan 36 (10), pp. 2335–2342 (Japanese).
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17: 13.3 Recurrence Relations and Derivatives
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§13.3(i) Recurrence Relations
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13.3.7
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13.3.14
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§13.3(ii) Differentiation Formulas
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13.3.29
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18: 13.5 Continued Fractions
19: 16.6 Transformations of Variable
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16.6.2
►For Kummer-type transformations of
functions see Miller (2003) and Paris (2005a), and for further transformations see Erdélyi et al. (1953a, §4.5), Miller and Paris (2011), Choi and Rathie (2013) and Wang and Rathie (2013).
20: 6.20 Approximations
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Luke (1969b, p. 25) gives a Chebyshev expansion near infinity for the confluent hypergeometric -function (§13.2(i)) from which Chebyshev expansions near infinity for , , and follow by using (6.11.2) and (6.11.3). Luke also includes a recursion scheme for computing the coefficients in the expansions of the functions. If the scheme can be used in backward direction.