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Minkowski's question mark function is the function y=?(x) defined by Minkowski for the purpose of mapping the quadratic surds in the open interval (0,1) into the rational ...

A differential equation is an equation that involves the derivatives of a function as well as the function itself. If partial derivatives are involved, the equation is called ...

In conical coordinates, Laplace's equation can be written ...

In elliptic cylindrical coordinates, the scale factors are h_u=h_v=sqrt(sinh^2u+sin^2v), h_z=1, and the separation functions are f_1(u)=f_2(v)=f_3(z)=1, giving a Stäckel ...

In parabolic cylindrical coordinates, the scale factors are h_u=h_v=sqrt(u^2+v^2), h_z=1 and the separation functions are f_1(u)=f_2(v)=f_3(z)=1, giving Stäckel determinant ...

In conical coordinates, Laplace's equation can be written ...

Write down the positive integers in row one, cross out every k_1th number, and write the partial sums of the remaining numbers in the row below. Now cross off every k_2th ...

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 ...

The Rogers-Ramanujan continued fraction is a generalized continued fraction defined by R(q)=(q^(1/5))/(1+q/(1+(q^2)/(1+(q^3)/(1+...)))) (1) (Rogers 1894, Ramanujan 1957, ...

Generalizing from a straight line (i.e., first degree polynomial) to a kth degree polynomial y=a_0+a_1x+...+a_kx^k, (1) the residual is given by ...