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The first and second Pöschl-Teller differential equations are given by y^('')-{a^2[(kappa(kappa-1))/(sin^2(ax))+(lambda(lambda-1))/(cos^2(ax))]-b^2}y=0 and ...

The system of partial differential equations u_(xx)-u_(yy)+/-sinucosu+(cosu)/(sin^3u)(v_x^2-v_y^2)=0 (v_xcot^2u)_x=(v_ycot^2u)_y.

Solutions to holomorphic differential equations are themselves holomorphic functions of time, initial conditions, and parameters.

To find the minimum distance between a point in the plane (x_0,y_0) and a quadratic plane curve y=a_0+a_1x+a_2x^2, (1) note that the square of the distance is r^2 = ...

D_P(x)=lim_(epsilon->0)(lnmu(B_epsilon(x)))/(lnepsilon), where B_epsilon(x) is an n-dimensional ball of radius epsilon centered at x and mu is the probability measure.

The ordinary differential equation y^('')+k/xy^'+deltae^y=0.

rho_n(nu,x)=((1+nu-n)_n)/(sqrt(n!x^n))_1F_1(-n;1+nu-n;x), where (a)_n is a Pochhammer symbol and _1F_1(a;b;z) is a confluent hypergeometric function of the first kind.

For R[nu]>-1/2, J_nu(z)=(z/2)^nu2/(sqrt(pi)Gamma(nu+1/2))int_0^(pi/2)cos(zcost)sin^(2nu)tdt, where J_nu(z) is a Bessel function of the first kind, and Gamma(z) is the gamma ...

A polynomial function is a function whose values can be expressed in terms of a defining polynomial. A polynomial function of maximum degree 0 is said to be a constant ...

The partial differential equation u_t=del ·(u^mdel u).