q-Leibniz rule
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11—20 of 34 matching pages
11: 34.7 Basic Properties: Symbol
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►This equation is the sum rule.
It constitutes an addition theorem for the symbol.
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12: 1.4 Calculus of One Variable
13: 1.11 Zeros of Polynomials
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Descartes’ Rule of Signs
…14: Bibliography
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Numerical computation of Tricomi’s psi function by the trapezoidal rule.
Computing 39 (3), pp. 271–279.
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Numerical evaluation of the Kummer function with complex argument by the trapezoidal rule.
Rend. Sem. Mat. Univ. Politec. Torino 49 (3), pp. 315–327.
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Numerical calculation of incomplete gamma functions by the trapezoidal rule.
Numer. Math. 50 (4), pp. 419–428.
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Numerical Calculation of the Riemann Zeta Function and Generalizations by Means of the Trapezoidal Rule.
In Numerical and Applied Mathematics, Part II (Paris, 1988), C. Brezinski (Ed.),
IMACS Ann. Comput. Appl. Math., Vol. 1, pp. 467–472.
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15: Bibliography G
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Stable computation of high order Gauss quadrature rules using discretization for measures in radiation transfer.
J. Quant. Spectrosc. Radiat. Transfer 68 (2), pp. 213–223.
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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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Computing special functions by using quadrature rules.
Numer. Algorithms 33 (1-4), pp. 265–275.
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Calculation of Gauss quadrature rules.
Math. Comp. 23 (106), pp. 221–230.
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16: 3.7 Ordinary Differential Equations
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►The method consists of a set of rules each of which is equivalent to a truncated Taylor-series expansion, but the rules avoid the need for analytic differentiations of the differential equation.
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►For the standard fourth-order rule reads
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►For the standard fourth-order rule reads
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17: 6.18 Methods of Computation
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►Zeros of and can be computed to high precision by Newton’s rule (§3.8(ii)), using values supplied by the asymptotic expansion (6.13.2) as initial approximations.
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18: 3.10 Continued Fractions
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►We continue by means of the rhombus rule
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19: 1.6 Vectors and Vector-Valued Functions
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►where is the unit vector normal to and whose direction is determined by the right-hand rule; see Figure 1.6.1.
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