relation%20to%20error%20functions
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11—16 of 16 matching pages
11: Bibliography K
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Algorithm 737: INTLIB: A portable Fortran 77 interval standard-function library.
ACM Trans. Math. Software 20 (4), pp. 447–459.
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Methods of computing the Riemann zeta-function and some generalizations of it.
USSR Comput. Math. and Math. Phys. 20 (6), pp. 212–230.
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Cyclic identities for Jacobi elliptic and related functions.
J. Math. Phys. 44 (4), pp. 1822–1841.
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Theta relations and projective normality of Abelian varieties.
Amer. J. Math. 98 (4), pp. 865–889.
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Algorithm 421. Complex gamma function with error control.
Comm. ACM 15 (4), pp. 271–272.
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12: 8.17 Incomplete Beta Functions
§8.17 Incomplete Beta Functions
… ►However, in the case of §8.17 it is straightforward to continue most results analytically to other real values of , , and , and also to complex values. … ►§8.17(ii) Hypergeometric Representations
… ►§8.17(iv) Recurrence Relations
… ►§8.17(vii) Addendum to 8.17(i) Definitions and Basic Properties
…13: Bibliography M
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Two-point quasi-fractional approximations to the Airy function
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J. Comput. Phys. 99 (2), pp. 337–340.
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Uniform computation of the error function and other related functions.
Math. Comp. 25 (114), pp. 339–344.
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Calculation of the modified Bessel functions of the second kind with complex argument.
Math. Comp. 20 (95), pp. 407–412.
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Evaluation of complex logarithms and related functions.
SIAM J. Numer. Anal. 18 (4), pp. 744–750.
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A new symmetry related to
for classical basic hypergeometric series.
Adv. in Math. 57 (1), pp. 71–90.
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14: Bibliography C
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The inverse of the error function.
Pacific J. Math. 13 (2), pp. 459–470.
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Calcolo delle funzioni speciali , , , , alle alte precisioni.
Atti Accad. Sci. Lett. Arti Palermo Ser. (5) 2(1981/82) (1), pp. 7–25 (Italian).
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Rational Chebyshev approximations for the error function.
Math. Comp. 23 (107), pp. 631–637.
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Performance evaluation of programs related to the real gamma function.
ACM Trans. Math. Software 17 (1), pp. 46–54.
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Validated computation of certain hypergeometric functions.
ACM Trans. Math. Software 38 (2), pp. Art. 11, 20.
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15: Bibliography O
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Summing one- and two-dimensional series related to the Euler series.
J. Comput. Appl. Math. 98 (2), pp. 245–271.
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An error analysis of the modified Clenshaw method for evaluating Chebyshev and Fourier series.
J. Inst. Math. Appl. 20 (3), pp. 379–391.
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Error analysis of Miller’s recurrence algorithm.
Math. Comp. 18 (85), pp. 65–74.
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Error bounds for stationary phase approximations.
SIAM J. Math. Anal. 5 (1), pp. 19–29.
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Asymptotic approximations and error bounds.
SIAM Rev. 22 (2), pp. 188–203.
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16: 19.36 Methods of Computation
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►Legendre’s integrals can be computed from symmetric integrals by using the relations in §19.25(i).
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►To (19.36.6) add
…If the iteration of (19.36.6) and (19.36.12) is stopped when ( and being approximated by and , and the infinite series being truncated), then the relative error in and is less than if we neglect terms of order .
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