negative%20definite
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1: 34.5 Basic Properties: Symbol
2: Bibliography
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Exact linearization of a Painlevé transcendent.
Phys. Rev. Lett. 38 (20), pp. 1103–1106.
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Polygamma functions of negative order.
J. Comput. Appl. Math. 100 (2), pp. 191–199.
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On the degrees of irreducible factors of higher order Bernoulli polynomials.
Acta Arith. 62 (4), pp. 329–342.
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Repeated integrals and derivatives of Bessel functions.
SIAM J. Math. Anal. 20 (1), pp. 169–175.
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Table of Definite and Infinite Integrals.
Physical Sciences Data, Vol. 13, Elsevier Scientific Publishing Co., Amsterdam.
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3: Bibliography G
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Algorithm 726: ORTHPOL — a package of routines for generating orthogonal polynomials and Gauss-type quadrature rules.
ACM Trans. Math. Software 20 (1), pp. 21–62.
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Algorithm 969: computation of the incomplete gamma function for negative values of the argument.
ACM Trans. Math. Softw. 43 (3), pp. 26:1–26:9.
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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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Definite integrals of the complete elliptic integral
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J. Res. Nat. Bur. Standards Sect. B 80B (2), pp. 313–323.
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Mutual integrability, quadratic algebras, and dynamical symmetry.
Ann. Phys. 217 (1), pp. 1–20.
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4: 10.3 Graphics
5: 25.7 Integrals
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βΊFor definite integrals of the Riemann zeta function see Prudnikov et al. (1986b, §2.4), Prudnikov et al. (1992a, §3.2), and Prudnikov et al. (1992b, §3.2).
6: 34.8 Approximations for Large Parameters
7: Bibliography N
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On an integral transform involving a class of Mathieu functions.
SIAM J. Math. Anal. 20 (6), pp. 1500–1513.
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Reduction and evaluation of elliptic integrals.
Math. Comp. 20 (94), pp. 223–231.
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A table of integrals of the error functions.
J. Res. Nat. Bur. Standards Sect B. 73B, pp. 1–20.
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COULN, a program for evaluating negative energy Coulomb functions.
Comput. Phys. Comm. 33 (4), pp. 413–419.
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Evaluation of negative energy Coulomb (Whittaker) functions.
Comput. Phys. Comm. 159 (1), pp. 55–62.
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8: Sidebar 5.SB1: Gamma & Digamma Phase Plots
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βΊThe color encoded phases of (above) and (below), are constrasted in the negative half of the complex plane.
βΊIn the upper half of the image, the poles of are clearly visible at negative integer values of : the phase changes by around each pole, showing a full revolution of the color wheel.
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9: 12.11 Zeros
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βΊFor large negative values of the real zeros of , , , and can be approximated by reversion of the Airy-type asymptotic expansions of §§12.10(vii) and 12.10(viii).
…Here , denoting the th negative zero of the function (see §9.9(i)).
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βΊwhere , denoting the th negative zero of the function and
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12.11.9
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