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An entire function which is a generalization of the Bessel function of the first kind defined by J_nu(z)=1/piint_0^picos(nutheta-zsintheta)dtheta. Anger's original function ...

The mathematical study of how given quantities can be approximated by other (usually simpler) ones under appropriate conditions. Approximation theory also studies the size ...

The associated Legendre polynomials P_l^m(x) and P_l^(-m)(x) generalize the Legendre polynomials P_l(x) and are solutions to the associated Legendre differential equation, ...

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 ...

The mathematical study of abstract computing machines (especially Turing machines) and the analysis of algorithms used by such machines. A connection between automata theory ...

The class of continuous functions is called the Baire class 0. For each n, the functions that can be considered as pointwise limits of sequences of functions of Baire class ...

If a contour in the complex plane is curved such that it separates the increasing and decreasing sequences of poles, then ...

The Baum-Sweet sequence is the sequence of numbers {b_n} such that b_n=1 if the binary representation of n contains no block of consecutive 0s of odd length, and b_n=0 ...

The Bessel functions of the first kind J_n(x) are defined as the solutions to the Bessel differential equation x^2(d^2y)/(dx^2)+x(dy)/(dx)+(x^2-n^2)y=0 (1) which are ...

A C^infty function is a function that is differentiable for all degrees of differentiation. For instance, f(x)=e^(2x) (left figure above) is C^infty because its nth ...