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21: 36.8 Convergent Series Expansions
22: 9.11 Products
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9.11.1
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►For example, , , , .
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9.11.10
►For , , , where is any positive integer, see Albright (1977).
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►For further definite integrals see Prudnikov et al. (1990, §1.8.2), Laurenzi (1993), Reid (1995, 1997a, 1997b), and Vallée and Soares (2010, Chapters 3, 4).
23: 17.9 Further Transformations of Functions
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§17.9(i) , , or
… ►§17.9(ii)
►Transformations of -Series
… ►Sears’ Balanced Transformations
►With …24: 31.2 Differential Equations
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►where and with are generators of the lattice for .
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►Lastly, satisfies (31.2.1) if is a solution of (31.2.1) with transformed parameters ; , , .
By composing these three steps, there result possible transformations of the dependent variable (including the identity transformation) that preserve the form of (31.2.1).
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►If is one of the homographies that map to , then satisfies (31.2.1) if is a solution of (31.2.1) with replaced by and appropriately transformed parameters.
…If is one of the homographies that do not map to , then an appropriate prefactor must be included on the right-hand side.
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25: 29.2 Differential Equations
26: 19.34 Mutual Inductance of Coaxial Circles
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19.34.1
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19.34.3
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►Application of (19.29.4) and (19.29.7) with , , , and yields
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19.34.5
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27: 23.6 Relations to Other Functions
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►In this subsection , are any pair of generators of the lattice , and the lattice roots , , are given by (23.3.9).
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►Again, in Equations (23.6.16)–(23.6.26), are any pair of generators of the lattice and are given by (23.3.9).
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►Let be on the perimeter of the rectangle with vertices .
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►Let be a point of different from , and define by
…where the integral is taken along any path from to that does not pass through any of .
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