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In three dimensions, the spherical harmonic differential equation is given by ...

Using the notation of Byerly (1959, pp. 252-253), Laplace's equation can be reduced to (1) where alpha = cint_c^lambda(dlambda)/(sqrt((lambda^2-b^2)(lambda^2-c^2))) (2) = ...

Wallis's constant is the real solution (x^3-2x-5)_1=2.0945514815... (OEIS A007493) to the cubic equation x^3-2x-5=0. It was solved by Wallis to illustrate Newton's method for ...

The ordinary differential equation (x^py^')^'+/-x^sigmay^n=0.

In conical coordinates, Laplace's equation can be written ...

The scale factors are h_u=h_v=sqrt(u^2+v^2), h_theta=uv and the separation functions are f_1(u)=u, f_2(v)=v, f_3(theta)=1, given a Stäckel determinant of S=u^2+v^2. The ...

In conical coordinates, Laplace's equation can be written ...

Spinor fields describing particles of zero rest mass satisfy the so-called zero rest mass equations. Examples of zero rest mass particles include the neutrino (a fermion) and ...

As a consequence of Matiyasevich's refutation of Hilbert's 10th problem, it can be proved that there does not exist a general algorithm for solving a general quartic ...

The 5.1.2 fifth-order Diophantine equation A^5=B^5+C^5 (1) is a special case of Fermat's last theorem with n=5, and so has no solution. improving on the results on Lander et ...