backward%20recursion
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21—30 of 140 matching pages
21: Bibliography G
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Recursive computation of the repeated integrals of the error function.
Math. Comp. 15 (75), pp. 227–232.
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A note on the recursive calculation of incomplete gamma functions.
ACM Trans. Math. Software 25 (1), pp. 101–107.
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The ABC of hyper recursions.
J. Comput. Appl. Math. 190 (1-2), pp. 270–286.
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Numerically satisfactory solutions of hypergeometric recursions.
Math. Comp. 76 (259), pp. 1449–1468.
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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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22: Mathematical Introduction
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complex plane (excluding infinity). | |
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(or ) | backward difference operator: . (See also del operator in the Notations section.) |
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23: Bibliography W
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The Nahm equations, finite-gap potentials and Lamé functions.
J. Phys. A 20 (10), pp. 2679–2683.
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Recursion formulae for hypergeometric functions.
Math. Comp. 22 (102), pp. 363–373.
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Algorithm 44: Bessel functions computed recursively.
Comm. ACM 4 (4), pp. 177–178.
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Upon systems of recursions which obtain among the quotients of the Padé table.
Numer. Math. 8 (3), pp. 264–269.
24: 29.6 Fourier Series
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►This solution can be constructed from (29.6.4) by backward recursion, starting with and an arbitrary nonzero value of , followed by normalization via (29.6.5) and (29.6.6).
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25: Bibliography L
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Algorithm 917: complex double-precision evaluation of the Wright function.
ACM Trans. Math. Software 38 (3), pp. Art. 20, 17.
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An asymptotic estimate for the Bernoulli and Euler numbers.
Canad. Math. Bull. 20 (1), pp. 109–111.
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Co-recursive associated Jacobi polynomials.
J. Comput. Appl. Math. 57 (1-2), pp. 203–213.
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New recursion relation for the Clebsch-Gordan coefficients.
Phys. Rev. (2) 110 (4), pp. 815–816.
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Simplified recursive algorithm for Wigner and symbols.
Phys. Rev. E 57 (6), pp. 7274–7277.
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26: 15.19 Methods of Computation
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►For example, in the half-plane we can use (15.12.2) or (15.12.3) to compute and , where is a large positive integer, and then apply (15.5.18) in the backward direction.
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27: 18.19 Hahn Class: Definitions
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Hahn class (or linear lattice class). These are OP’s where the role of is played by or or (see §18.1(i) for the definition of these operators). The Hahn class consists of four discrete and two continuous families.
Wilson class (or quadratic lattice class). These are OP’s ( of degree in , quadratic in ) where the role of the differentiation operator is played by or or . The Wilson class consists of two discrete and two continuous families.
28: 34.13 Methods of Computation
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►Methods of computation for and symbols include recursion relations, see Schulten and Gordon (1975a), Luscombe and Luban (1998), and Edmonds (1974, pp. 42–45, 48–51, 97–99); summation of single-sum expressions for these symbols, see Varshalovich et al. (1988, §§8.2.6, 9.2.1) and Fang and Shriner (1992); evaluation of the generalized hypergeometric functions of unit argument that represent these symbols, see Srinivasa Rao and Venkatesh (1978) and Srinivasa Rao (1981).
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29: Bibliography F
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Sur certaines sommes des intégral-cosinus.
Bull. Soc. Math. Phys. Serbie 12, pp. 13–20 (French).
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Tables of Elliptic Integrals of the First, Second, and Third Kind.
Technical report
Technical Report ARL 64-232, Aerospace Research Laboratories, Wright-Patterson Air Force Base, Ohio.
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On weighted polynomial approximation on the whole real axis.
Acta Math. Acad. Sci. Hungar. 20, pp. 223–225.
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On the coefficients in the recursion formulae of orthogonal polynomials.
Proc. Roy. Irish Acad. Sect. A 76 (1), pp. 1–6.
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30: Bibliography S
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Transformations of the Jacobian amplitude function and its calculation via the arithmetic-geometric mean.
SIAM J. Math. Anal. 20 (6), pp. 1514–1528.
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Recursive evaluation of - and - coefficients.
Comput. Phys. Comm. 11 (2), pp. 269–278.
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Exact recursive evaluation of - and -coefficients for quantum-mechanical coupling of angular momenta.
J. Mathematical Phys. 16 (10), pp. 1961–1970.
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Uniform asymptotic forms of modified Mathieu functions.
Quart. J. Mech. Appl. Math. 20 (3), pp. 365–380.
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A Maple package for symmetric functions.
J. Symbolic Comput. 20 (5-6), pp. 755–768.
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