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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 Helmholtz differential equation in spherical coordinates is separable. In fact, it is separable under the more general condition that k^2 is of the form ...

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

The Frobenius number is the largest value b for which the Frobenius equation a_1x_1+a_2x_2+...+a_nx_n=b, (1) has no solution, where the a_i are positive integers, b is an ...

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

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 ...

A unitary perfect number is a number n which is the sum of its unitary divisors with the exception of n itself. There are no odd unitary perfect numbers, and it has been ...

A number n is called wasteful if the number of digits in the prime factorization of n (including powers) uses more digits than the number of digits in n. The first few ...

The Euler numbers, also called the secant numbers or zig numbers, are defined for |x|<pi/2 by sechx-1=-(E_1^*x^2)/(2!)+(E_2^*x^4)/(4!)-(E_3^*x^6)/(6!)+... (1) ...

An even number of the form 4n+2 (i.e., an integer which is divisible by 2 but not by 4). The first few for n=0, 1, 2, ... are 2, 6, 10, 14, 18, ... (OEIS A016825)