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The symbol defined by c^(a/b) = c(c+b)(c+2b)...[c+(a-1)b] (1) = b^a(c/b)_a (2) = (b^aGamma(a+c/b))/(Gamma(c/b)), (3) where (a)_n is the Pochhammer symbol and Gamma(z) is 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 ...

A reflection relation is a functional equation relating f(-x) to f(x), or more generally, f(a-x) to f(x). Perhaps the best known example of a reflection formula is the gamma ...

Let M be an oriented regular surface in R^3 with normal N. Then the support function of M is the function h:M->R defined by h(p)=p·N(p).

The Chebyshev integral is given by intx^p(1-x)^qdx=B(x;1+p,1+q), where B(x;a,b) is an incomplete beta function.

A generalization of the Euler L-function associated with a Grössencharakter.

A polynomial function is a function whose values can be expressed in terms of a defining polynomial. A polynomial function of maximum degree 0 is said to be a constant ...

A smooth function is a function that has continuous derivatives up to some desired order over some domain. A function can therefore be said to be smooth over a restricted ...

A function f such that |f(x)-f(y)|<=C|x-y| for all x and y, where C is a constant independent of x and y, is called a Lipschitz function. For example, any function with a ...

The Coulomb wave function is a special case of the confluent hypergeometric function of the first kind. It gives the solution to the radial Schrödinger equation in the ...