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21—30 of 65 matching pages
21: 1.13 Differential Equations
22: 18.23 Hahn Class: Generating Functions
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23: 20.11 Generalizations and Analogs
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►With the substitutions
, , with , we have
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24: 28.33 Physical Applications
25: 14.5 Special Values
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26: 10.41 Asymptotic Expansions for Large Order
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►To establish (10.41.12) we substitute into (10.34.3), with and replaced by , by means of (10.41.13) observing that when is large the effect of replacing by is to replace , , and by , , and , respectively.
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►Lastly, we substitute into (10.4.4), again with replaced by .
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27: 18.9 Recurrence Relations and Derivatives
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►Further -th derivative formulas relating two different Jacobi polynomials can be obtained from §15.5(i) by substitution of (18.5.7).
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►Further -th derivative formulas relating two different Laguerre polynomials can be obtained from §13.3(ii) by substitution of (13.6.19).
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28: 18.17 Integrals
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►Formula (18.17.9), after substitution of (18.5.7), is a special case of (15.6.8).
Formulas (18.17.9), (18.17.10) and (18.17.11) are fractional generalizations of -th derivative formulas which are, after substitution of (18.5.7), special cases of (15.5.4), (15.5.5) and (15.5.3), respectively.
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►Formulas (18.17.14) and (18.17.15) are fractional generalizations of -th derivative formulas which are, after substitution of (13.6.19), special cases of (13.3.18) and (13.3.20), respectively.
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►
18.17.21_1
, ,
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►
18.17.34_5
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29: 4.13 Lambert -Function
30: 10.18 Modulus and Phase Functions
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