Kelvin-function analogs
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21—30 of 56 matching pages
21: Bibliography M
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A -analog of the summation theorem for hypergeometric series well-poised in
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Adv. in Math. 57 (1), pp. 14–33.
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A -analog of hypergeometric series well-poised in and invariant -functions.
Adv. in Math. 58 (1), pp. 1–60.
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A -analog of the Gauss summation theorem for hypergeometric series in
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Adv. in Math. 72 (1), pp. 59–131.
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A -analog of a Whipple’s transformation for hypergeometric series in
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Adv. Math. 108 (1), pp. 1–76.
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22: 10.67 Asymptotic Expansions for Large Argument
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§10.67(i) , and Derivatives
… ►The contributions of the terms in , , , and on the right-hand sides of (10.67.3), (10.67.4), (10.67.7), and (10.67.8) are exponentially small compared with the other terms, and hence can be neglected in the sense of Poincaré asymptotic expansions (§2.1(iii)). … ►§10.67(ii) Cross-Products and Sums of Squares in the Case
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10.67.10
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23: 5.18 -Gamma and -Beta Functions
24: 10.25 Definitions
25: 10.38 Derivatives with Respect to Order
26: 10.74 Methods of Computation
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►Similarly, to maintain stability in the interval the integration direction has to be forwards in the case of and backwards in the case of , with initial values obtained in an analogous manner to those for and .
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27: 17.9 Further Transformations of Functions
28: 19.4 Derivatives and Differential Equations
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►An analogous differential equation of third order for is given in Byrd and Friedman (1971, 118.03).
29: 19.33 Triaxial Ellipsoids
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►Application of (19.16.23) transforms the last quantity in (19.30.5) into a two-dimensional analog of (19.33.1).
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