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Laplace's integral is one of the following integral representations of the Legendre polynomial P_n(x), P_n(x) = 1/piint_0^pi(du)/((x+sqrt(x^2-1)cosu)^(n+1))du (1) = ...

Let q be a positive integer, then Gamma_0(q) is defined as the set of all matrices [a b; c d] in the modular group Gamma Gamma with c=0 (mod q). Gamma_0(q) is a subgroup of ...

F(x,s) = sum_(m=1)^(infty)(e^(2piimx))/(m^s) (1) = psi_s(e^(2piix)), (2) where psi_s(x) is the polygamma function.

A^*(x)=sum_(lambda_n<=x)^'a_n=1/(2pii)int_(c-iinfty)^(c+iinfty)f(s)(e^(sx))/sds, where f(s)=suma_ne^(-lambda_ns).

The symbol tau (the lower case Greek letter tau) has many common uses in mathematics, as summarized in the following table. 1. tau(n) is an alternate notation for the divisor ...

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 ...

The number of poles of an automorphic function in the closure of its fundamental region.

Arrow's paradox, also called Arrow's impossibility theorem or the general possibility theorem, states that perfect democratic voting is impossible, not just in practice but ...

The conditional probability of an event A assuming that B has occurred, denoted P(A|B), equals P(A|B)=(P(A intersection B))/(P(B)), (1) which can be proven directly using a ...

The property of being continuous.