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A generalization of the Bessel differential equation for functions of order 0, given by zy^('')+y^'+(z+A)y=0. Solutions are y=e^(+/-iz)_1F_1(1/2∓1/2iA;1;∓2iz), where ...

Two circles with centers at (x_i,y_i) with radii r_i for i=1,2 are mutually tangent if (x_1-x_2)^2+(y_1-y_2)^2=(r_1+/-r_2)^2. (1) If the center of the second circle is inside ...

One baud is defined as the state of a signal in a communication channel changing once per second.

If a minimal surface is given by the equation z=f(x,y) and f has continuous first and second partial derivatives for all real x and y, then f is a plane.

The second-order ordinary differential equation (x^2y^')^'+x^2y^n=0.

The second-order ordinary differential equation y^('')+k/xy^'+epsilony^'y=0.

The second-order ordinary differential equation y^('')+alpha(x)y^'+x^2y^n=0.

The second-order ordinary differential equation satisfied by the Neumann polynomials O_n(x).

The second-order ordinary differential equation y^('')+[A+Bcos(2x)+Ccos(4x)]y=0.

Turing machines are defined by sets of rules that operate on four parameters: (state, tape cell color, operation, state). Let the states and tape cell colors be numbered and ...