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For R[z]>0, where J_nu(z) is a Bessel function of the first kind.

The function Pi_(a,b)(x)=H(x-a)-H(x-b) which is equal to 1 for a<=x<=b and 0 otherwise. Here H(x) is the Heaviside step function. The special case Pi_(-1/2,1/2)(x) gives the ...

A function or transformation f in which f(z) does not overlap z. In modular function theory, a function is called univalent on a subgroup G if it is automorphic under G and ...

(e^(ypsi_0(x))Gamma(x))/(Gamma(x+y))=product_(n=0)^infty(1+y/(n+x))e^(-y/(n+x)), where psi_0(x) is the digamma function and Gamma(x) is the gamma function.

The number of representations of n by k squares, allowing zeros and distinguishing signs and order, is denoted r_k(n). The special case k=2 corresponding to two squares is ...

A function f(x) is said to be strictly decreasing on an interval I if f(b)<f(a) for all b>a, where a,b in I. On the other hand, if f(b)<=f(a) for all b>a, the function is ...

A function f(x) is said to be strictly increasing on an interval I if f(b)>f(a) for all b>a, where a,b in I. On the other hand, if f(b)>=f(a) for all b>a, the function is ...

A univariate function f(x) is said to be even provided that f(x)=f(-x). Geometrically, such functions are symmetric about the y-axis. Examples of even functions include 1 ...

There are two types of singular values, one in the context of elliptic integrals, and the other in linear algebra. For a square matrix A, the square roots of the eigenvalues ...

The (complete) gamma function Gamma(n) is defined to be an extension of the factorial to complex and real number arguments. It is related to the factorial by Gamma(n)=(n-1)!, ...