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- ...ral''' of function \(f\) is function \(J^n f\) expressed with iteration of integration: ==Cauchi representation for the iterated integration==9 KB (1,321 words) - 18:26, 30 July 2019
- ...e included "as is" to the [[C++]] code for the numerical implementation of integration. This file is used in the generators of figures for the [[Cauchi integral]] [[Integration]], [[Tetration]], [[C++]]108 KB (1,626 words) - 18:46, 30 July 2019
- ==Numerical Implementation of ArcSin== The appropriate contour of integration may go straight from zero to \(z\).9 KB (982 words) - 18:48, 30 July 2019
- ==Numerical implementation== With new variable of integration \(y=x_n\),3 KB (421 words) - 18:26, 30 July 2019
- The polynomial is good function for the analytic integration with exponential; so, the representation with the truncated series above ca ..., but exact mathematical constant). Similar goal can be formulated for the numerical implementation of other [[special function]]s.13 KB (1,759 words) - 18:45, 30 July 2019
- If \(N\!=\!2^n\) for some integer \(n\), then, there exist efficient numerical algorithms for evaluation of this sum. One of them is called cosft1 and described in the [[Numerical recipes in C]]; it is available online, as well as the similar algorithm go5 KB (721 words) - 18:44, 30 July 2019
- seems to be efficient in the numerical calculations with approximation of atomic wave functions in spherical coord [[Category:Numerical integration]]7 KB (997 words) - 18:44, 30 July 2019
- ...used for the modification of the formulas above for arbitrary interval of integration. One example adopted from the [[Numerical recipes in C]] is shown below:3 KB (486 words) - 18:47, 30 July 2019
- The upper curve, \(y=\mathrm{A}(x)\), shows, that at the integration of square of this approximation from zero to at least 42 with a complex exp This estimate is important for approximation and numerical implementation of function [[naga]],14 KB (1,943 words) - 18:48, 30 July 2019
- elaborated for the numerical implementation of integrals with function [[nori]]\((x)=\,\)[[kori]]\((x)^2 In particular, the upper curve, \(y=\mathrm{A}(x)\), shows, that at the integration with this approximation from zero to at least 42 with a complex exponent, t4 KB (644 words) - 18:47, 30 July 2019
- The [[Gauss-Laguerre quadrature]] formula for the numerical integration of a smooth function ...k\), the \(k\)th Laguerre functions also form the orthogonal basis at the integration with the exponential weight:5 KB (759 words) - 18:44, 30 July 2019
- Precise evaluation of constant \(C_0\) requires either integration of oscillating function (that is slow, if performed in a straightforward wa Then, the change of variable of integration definition of function [[naga]] becomes straightforward. Let \(q=p^2\); the8 KB (1,256 words) - 18:44, 30 July 2019
- ...\!=\!1\), so, no special expansion at unity happen to be necessary for the numerical implementation. ...tter precision, than the original representation in the definition and the numerical implementation in the C++ built-in function double j0(double x).15 KB (2,303 words) - 18:47, 30 July 2019
- The integration gives the identity ...sting process stops. The "missed" data may be set to zero; this allows the numerical approximations of the formulas above with finite number of operations. Fini6 KB (944 words) - 18:48, 30 July 2019
- ...of [[numerical integration]]. Many widely used formulas for the numerical integration appear at consideration of specific orthogonal polynomials. In particular, and \(b\!=\!\infty\). Namely for this case, the numerical integration is required for evaluation of the contour integral for function [[naga]].6 KB (918 words) - 18:47, 30 July 2019
- 5. Numerical implementation, that allows to evaluate the function with several decimal d ...ften, before of define correctly the complex numbers, differentiation, and integration.7 KB (991 words) - 18:48, 30 July 2019
