double products
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21: 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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Asymptotic and numeric study of eigenvalues of the double confluent Heun equation.
J. Phys. A 31 (42), pp. 8521–8531.
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Numerical evaluation of integrals containing a spherical Bessel function by product integration.
J. Math. Phys. 22 (7), pp. 1399–1413.
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A note on the computation of integrals involving products of trigonometric and Bessel functions.
Math. Comp. 27 (124), pp. 871–872.
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Evaluating infinite integrals involving products of Bessel functions of arbitrary order.
J. Comput. Appl. Math. 64 (3), pp. 269–282.
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22: 3.8 Nonlinear Equations
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►After a zero has been computed, the factor is factored out of as a by-product of Horner’s scheme (§1.11(i)) for the computation of .
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►As in the case of Table 3.8.1 the quadratic nature of convergence is clearly evident: as the zero is approached, the number of correct decimal places doubles at each iteration.
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23: Bibliography B
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Products of generalized hypergeometric series.
Proc. London Math. Soc. (2) 28 (2), pp. 242–254.
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Coulomb functions (negative energies).
Comput. Phys. Comm. 20 (3), pp. 447–458.
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The double confluent Heun equation: Characteristic exponent and connection formulae.
Methods Appl. Anal. 1 (3), pp. 348–370.
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Expansions of Appell’s double hypergeometric functions.
Quart. J. Math., Oxford Ser. 11, pp. 249–270.
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Expansions of Appell’s double hypergeometric functions. II.
Quart. J. Math., Oxford Ser. 12, pp. 112–128.
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24: Bibliography
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Algorithm 724: Program to calculate F-percentiles.
ACM Trans. Math. Software 19 (4), pp. 481–483.
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Integrals of products of Bernoulli polynomials.
J. Math. Anal. Appl. 381 (1), pp. 10–16.
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Integrals of products of Airy functions.
J. Phys. A 10 (4), pp. 485–490.
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Algorithm 804: Subroutines for the computation of Mathieu functions of integer orders.
ACM Trans. Math. Software 26 (3), pp. 408–414.
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An integral of products of ultraspherical functions and a -extension.
J. London Math. Soc. (2) 33 (1), pp. 133–148.
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25: 19.29 Reduction of General Elliptic Integrals
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►If
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19.29.3
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►Moreover, the requirement that one limit of integration be a branch point of the integrand is eliminated without doubling the number of standard integrals in the result.
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►where is any permutation of the numbers , and
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19.29.17
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26: Bibliography V
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Integrating products of Bessel functions with an additional exponential or rational factor.
Comput. Phys. Comm. 178 (8), pp. 578–590.
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Expansions in products of Heine-Stieltjes polynomials.
Constr. Approx. 15 (4), pp. 467–480.
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Integral representations for products of Lamé functions by use of fundamental solutions.
SIAM J. Math. Anal. 15 (3), pp. 559–569.
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RFSFNS: A portable package for the numerical determination of the number and the calculation of roots of Bessel functions.
Comput. Phys. Comm. 92 (2-3), pp. 252–266.
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27: Bibliography M
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On the zeros of cross-product Bessel functions.
J. Math. Mech. 16, pp. 447–452.
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On the evaluation of the integral over the product of two spherical Bessel functions.
J. Math. Phys. 32 (3), pp. 642–648.
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Analytic expressions for integrals of products of spherical Bessel functions.
J. Phys. A 24 (7), pp. 1435–1453.
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Further improvements of some double inequalities for bounding the gamma function.
Math. Comput. Modelling 57 (5-6), pp. 1360–1363.
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On the zeros of a cross-product of Bessel functions of different orders.
Z. Angew. Math. Mech. 59 (6), pp. 272–273.
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28: Bibliography K
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Numerical Methods and Software.
Prentice Hall, Englewood Cliffs, N.J..
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Jacobi polynomials. II. An analytic proof of the product formula.
SIAM J. Math. Anal. 5, pp. 125–137.
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The relationship between Zhedanov’s algebra and the double affine Hecke algebra in the rank one case.
SIGMA 3, pp. Paper 063, 15 pp..
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ZEBEC: A mathematical software package for computing simple zeros of Bessel functions of real order and complex argument.
Comput. Phys. Comm. 113 (2-3), pp. 220–238.
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29: Bibliography D
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Sums of products of Bernoulli numbers.
J. Number Theory 60 (1), pp. 23–41.
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Vector coupling coefficients as products of prime factors.
Comput. Phys. Comm. 4 (2), pp. 268–274.
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Uniform asymptotic solutions of second-order linear differential equations having a double pole with complex exponent and a coalescing turning point.
SIAM J. Math. Anal. 21 (6), pp. 1594–1618.
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Nicholson-type Integrals for Products of Gegenbauer Functions and Related Topics.
In Theory and Application of Special Functions (Proc. Advanced
Sem., Math. Res. Center, Univ. Wisconsin, Madison, Wis.,
1975), R. A. Askey (Ed.),
pp. 353–374. Math. Res. Center, Univ. Wisconsin, Publ. No. 35.
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Product formulas and Nicholson-type integrals for Jacobi functions. I. Summary of results.
SIAM J. Math. Anal. 9 (1), pp. 76–86.
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