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Yahtzee is a game played with five 6-sided dice. Players take turns rolling the dice, and trying to get certain types of rolls, each with an assigned point value, as ...

z(1-z)(d^2y)/(dz^2)+[c-(a+b+1)z](dy)/(dz)-aby=0. It has regular singular points at 0, 1, and infty. Every second-order ordinary differential equation with at most three ...

e^(izcostheta)=sum_(n=-infty)^inftyi^nJ_n(z)e^(intheta), where J_n(z) is a Bessel function of the first kind. The identity can also be written ...

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.