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In summary, the Tanh-Sinh quadrature scheme is designed so that it gives the most accurate result for the minimum number of function evaluations. In practice, the Tanh-Sinh quadrature rule is almost invariably the best rule and is often the only effective rule when extended precision results are sought [citation needed].
In mathematics, the Gauss map (also known as Gaussian map [1] or mouse map), is a nonlinear iterated map of the reals into a real interval given by the Gaussian function: x n + 1 = exp ( − α x n 2 ) + β , {\displaystyle x_{n+1}=\exp(-\alpha x_{n}^{2})+\beta ,\,}
SciPy (pronounced / ˈ s aɪ p aɪ / "sigh pie" [2]) is a free and open-source Python library used for scientific computing and technical computing. [3]SciPy contains modules for optimization, linear algebra, integration, interpolation, special functions, FFT, signal and image processing, ODE solvers and other tasks common in science and engineering.
Weights versus x i for four choices of n. In numerical analysis, Gauss–Hermite quadrature is a form of Gaussian quadrature for approximating the value of integrals of the following kind:
is the negative normalized second derivative of a Gaussian function, i.e., up to scale and normalization, the second Hermite function. It is a special case of the family of continuous wavelets (wavelets used in a continuous wavelet transform) known as Hermitian wavelets. The Ricker wavelet is frequently employed to model seismic data, and as a ...
In numerical analysis Gauss–Laguerre quadrature (named after Carl Friedrich Gauss and Edmond Laguerre) is an extension of the Gaussian quadrature method for approximating the value of integrals of the following kind: + (). In this case
SymPy is an open-source Python library for symbolic computation.It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live [2] or SymPy Gamma. [3]
Generalized hypergeometric functions include the (Gaussian) hypergeometric function and the confluent hypergeometric function as special cases, which in turn have many particular special functions as special cases, such as elementary functions, Bessel functions, and the classical orthogonal polynomials.