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The modified spherical Bessel differential equation is given by the spherical Bessel differential equation with a negative separation constant, ...

A generalization of the confluent hypergeometric differential equation given by (1) The solutions are given by y_1 = x^(-A)e^(-f(x))_1F_1(a;b;h(x)) (2) y_2 = ...

The generalized hypergeometric function F(x)=_pF_q[alpha_1,alpha_2,...,alpha_p; beta_1,beta_2,...,beta_q;x] satisfies the equation where theta=x(partial/partialx) is the ...

Take the Helmholtz differential equation del ^2F+k^2F=0 (1) in spherical coordinates. This is just Laplace's equation in spherical coordinates with an additional term, (2) ...

A second-order ordinary differential equation arising in the study of stellar interiors, also called the polytropic differential equations. It is given by ...

On the surface of a sphere, attempt separation of variables in spherical coordinates by writing F(theta,phi)=Theta(theta)Phi(phi), (1) then the Helmholtz differential ...

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 ...

Given a first-order ordinary differential equation (dy)/(dx)=F(x,y), (1) if F(x,y) can be expressed using separation of variables as F(x,y)=X(x)Y(y), (2) then the equation ...

Differential geometry is the study of Riemannian manifolds. Differential geometry deals with metrical notions on manifolds, while differential topology deals with nonmetrical ...

A differential ideal I on a manifold M is an ideal in the exterior algebra of differential k-forms on M which is also closed under the exterior derivative d. That is, for any ...