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The solutions to the Riemann P-differential equation are known as the Riemann P-series, or sometimes the Riemann P-function, given by u(z)=P{a b c; alpha beta gamma; alpha^' ...

A system of curvilinear coordinates for which several different notations are commonly used. In this work (u,v,phi) is used, whereas Arfken (1970) uses (xi,eta,phi) and Moon ...

Partial differential equation boundary conditions which give the value of the function on a surface, e.g., T=f(r,t).

Partial differential equation boundary conditions which give the normal derivative on a surface.

Given a system of ordinary differential equations of the form d/(dt)[x; y; v_x; v_y]=-[0 0 -1 0; 0 0 0 -1; Phi_(xx)(t) Phi_(yx)(t) 0 0; Phi_(xy)(t) Phi_(yy)(t) 0 0][x; y; ...

The Kiepert hyperbola is a hyperbola and triangle conic that is related to the solution of Lemoine's problem and its generalization to isosceles triangles constructed on the ...

The Mathieu functions are the solutions to the Mathieu differential equation (d^2V)/(dv^2)+[a-2qcos(2v)]V=0. (1) Even solutions are denoted C(a,q,v) and odd solutions by ...

There are three types of boundary conditions commonly encountered in the solution of partial differential equations: 1. Dirichlet boundary conditions specify the value of the ...

Let r and s be positive integers which are relatively prime and let a and b be any two integers. Then there is an integer N such that N=a (mod r) (1) and N=b (mod s). (2) ...

(x^2)/(a^2-lambda)+(y^2)/(b^2-lambda)=z-lambda (1) (x^2)/(a^2-mu)+(y^2)/(b^2-mu)=z-mu (2) (x^2)/(a^2-nu)+(y^2)/(b^2-nu)=z-nu, (3) where lambda in (-infty,b^2), mu in ...