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Given a Jacobi amplitude phi in an elliptic integral, the argument u is defined by the relation phi=am(u,k). It is related to the elliptic integral of the first kind F(u,k) ...

A parameter n used to specify an elliptic integral of the third kind Pi(n;phi,k).

An even Mathieu function ce_r(z,q) with characteristic value a_r.

delta(r)=sqrt(r)-2alpha(r), where alpha(r) is the elliptic alpha function.

E(a,b)/p denotes the elliptic group modulo p whose elements are 1 and infty together with the pairs of integers (x,y) with 0<=x,y<p satisfying y^2=x^3+ax+b (mod p) (1) with a ...

The second singular value k_2, corresponding to K^'(k_2)=sqrt(2)K(k_2), (1) is given by k_2 = tan(pi/8) (2) = sqrt(2)-1 (3) k_2^' = sqrt(2)(sqrt(2)-1). (4) For this modulus, ...

An odd Mathieu function se_r(z,q) with characteristic value a_r.

A catastrophe which can occur for three control factors and two behavior axes. The elliptical umbilic is catastrophe of codimension 3 that has the equation ...

The Elsasser function is defined by the integral E(y,u)=int_(-1/2)^(1/2)exp[-(2piyusinh(2piy))/(cosh(2piy)-cos(2pix))]dx. (1) Special values include E(0,u) = 1 (2) E(y,0) = ...

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