Evaluation of Associated Legendre Functions off the Cut and Parabolic Cylinder Functions∗
نویسنده
چکیده
We review a set of algorithms to evaluate associated Legendre functions off the cut; in particular, we consider prolate spheroidal, oblate spheroidal and toroidal harmonics. A similar scheme can be applied to other families of special functions like Bessel and parabolic cylinder functions; we will describe the corresponding algorithm for the evaluation of parabolic cylinder functions.
منابع مشابه
Kinetics of First Passage in a Cone
We study statistics of first passage inside a cone in arbitrary spatial dimension. The probability that a diffusing particle avoids the cone boundary decays algebraically with time. The decay exponent depends on two variables: the opening angle of the cone and the spatial dimension. In four dimensions, we find an explicit expression for the exponent, and in general, we obtain it as a root of a ...
متن کاملNumerical Solution of The Parabolic Equations by Variational Iteration Method and Radial Basis Functions
In this work, we consider the parabolic equation: $u_t-u_{xx}=0$. The purpose of this paper is to introduce the method of variational iteration method and radial basis functions for solving this equation. Also, the method is implemented to three numerical examples. The results reveal that the technique is very effective and simple.
متن کاملAnalysis of Test Day Milk Yield by Random Regression Models and Evaluation of Persistency in Iranian Dairy Cows
Variace / covariance components of 227118 first lactaiom test-day milk yield records belonged to 31258 Iranian Holstein cows were estimated using nine random regression models. Afterwards, different measures of persistency based on estimation breeding value were evaluated. Three functions were used to adjust fixed lactation curve: Ali and Schaeffer (AS), quadratic (LE3) and cubic (LE4) order of...
متن کاملUsing shifted Legendre scaling functions for solving fractional biochemical reaction problem
In this paper, biochemical reaction problem is given in the form of a system of non-linear differential equations involving Caputo fractional derivative. The aim is to suggest an instrumental scheme to approximate the solution of this problem. To achieve this goal, the fractional derivation terms are expanded as the elements of shifted Legendre scaling functions. Then, applying operational matr...
متن کاملOn bounds for solutions of monotonic first order difference-differential systems
Many special functions are solutions of first order linear systems y′ n(x) = an(x)yn(x) + dn(x)yn−1(x), y ′ n−1(x), = bn(x)yn−1(x) + en(x)yn(x) . We obtain bounds for the ratios yn(x)/yn-1(x) and the logarithmic derivatives of yn(x) for solutions of monotonic systems satisfying certain initial conditions. For the case dn(x)en(x) > 0, sequences of upper and lower bounds can be obtained by iterat...
متن کامل