representations%20as%20sums%20of%20powers
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1: 32.8 Rational Solutions
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►where the are monic polynomials (coefficient of highest power of is ) satisfying
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►For determinantal representations see Kajiwara and Masuda (1999).
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►For determinantal representations see Kajiwara and Ohta (1998) and Noumi and Yamada (1999).
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►For determinantal representations see Masuda et al. (2002).
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2: 19.36 Methods of Computation
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►When the differences are moderately small, the iteration is stopped, the elementary symmetric functions of certain differences are calculated, and a polynomial consisting of a fixed number of terms of the sum in (19.19.7) is evaluated.
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19.36.2
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►For computation of Legendre’s integral of the third kind, see Abramowitz and Stegun (1964, §§17.7 and 17.8, Examples 15, 17, 19, and 20).
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►Numerical quadrature is slower than most methods for the standard integrals but can be useful for elliptic integrals that have complicated representations in terms of standard integrals.
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►Faster convergence of power series for and can be achieved by using (19.5.1) and (19.5.2) in the right-hand sides of (19.8.12).
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3: Bibliography G
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Integral representations for computing real parabolic cylinder functions.
Numer. Math. 98 (1), pp. 105–134.
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Algorithm 939: computation of the Marcum Q-function.
ACM Trans. Math. Softw. 40 (3), pp. 20:1–20:21.
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Stirling number representation problems.
Proc. Amer. Math. Soc. 11 (3), pp. 447–451.
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A monotonicity property of the power function of multivariate tests.
Indag. Math. (N.S.) 11 (2), pp. 209–218.
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Representations of Integers as Sums of Squares.
Springer-Verlag, New York.
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