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The associated Legendre differential equation is a generalization of the Legendre differential equation given by d/(dx)[(1-x^2)(dy)/(dx)]+[l(l+1)-(m^2)/(1-x^2)]y=0, (1) which ...

Informally, the term asymptotic means approaching a value or curve arbitrarily closely (i.e., as some sort of limit is taken). A line or curve A that is asymptotic to given ...

Let n be an integer variable which tends to infinity and let x be a continuous variable tending to some limit. Also, let phi(n) or phi(x) be a positive function and f(n) or ...

An automorphism is an isomorphism of a system of objects onto itself. The term derives from the Greek prefix alphaupsilontauomicron (auto) "self" and ...

Let phi:M->M be a C^1 diffeomorphism on a compact Riemannian manifold M. Then phi satisfies Axiom A if the nonwandering set Omega(phi) of phi is hyperbolic and the periodic ...

Propositional calculus, first-order logic, and other theories in mathematical logic are defined by their axioms (or axiom schemata, plural: axiom schemata) and inference ...

A method of solving combinatorial problems by means of an algorithm which is allowed to run forward until a dead end is reached, at which point previous steps are retraced ...

A method which can be used to solve some classes of integral equations and is especially useful in implementing certain types of data inversion. It has been applied to invert ...

A Bäcklund transformation allows additional solutions to a nonlinear partial differential equations to be found if one particular solution is already known.

If, for n>=0, beta_n=sum_(r=0)^n(alpha_r)/((q;q)_(n-r)(aq;q)_(n+r)), (1) then beta_n^'=sum_(r=0)^n(alpha_r^')/((q;q)_(n-r)(aq;q)_(n+r)), (2) where alpha_r^' = ...