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The (associated) Legendre function of the first kind P_n^m(z) is the solution to the Legendre differential equation which is regular at the origin. For m,n integers and z ...

A point about which inversion of two circles produced concentric circles. Every pair of distinct circles has two limiting points. The limiting points correspond to the point ...

The continuous distribution with parameters m and b>0 having probability and distribution functions P(x) = (e^(-(x-m)/b))/(b[1+e^(-(x-m)/b)]^2) (1) D(x) = 1/(1+e^(-(x-m)/b)) ...

The Lommel polynomials R_(m,nu)(z) arise from the equation J_(m+nu)(z)=J_nu(z)R_(m,nu)(z)-J_(nu-1)(z)R_(m-1,nu+1)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

A predictor-corrector method for solution of ordinary differential equations. The third-order equations for predictor and corrector are y_(n+1) = ...

The modified Lommel functions of the first and second kind give the solution to the Lommel differential equation with a minus sign in front of the linear term, i.e., ...

A modular inverse of an integer b (modulo m) is the integer b^(-1) such that bb^(-1)=1 (mod m). A modular inverse can be computed in the Wolfram Language using PowerMod[b, ...

The Morgan-Voyce polynomials are polynomials related to the Brahmagupta and Fibonacci polynomials. They are defined by the recurrence relations b_n(x) = ...

The equation of incompressible fluid flow, (partialu)/(partialt)+u·del u=-(del P)/rho+nudel ^2u, where nu is the kinematic viscosity, u is the velocity of the fluid parcel, P ...

Polynomials O_n(x) that can be defined by the sum O_n(x)=1/4sum_(k=0)^(|_n/2_|)(n(n-k-1)!)/(k!)(1/2x)^(2k-n-1) (1) for n>=1, where |_x_| is the floor function. They obey the ...