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A generating function f(x) is a formal power series f(x)=sum_(n=0)^inftya_nx^n (1) whose coefficients give the sequence {a_0,a_1,...}. The Wolfram Language command ...

A function that arises in performance analysis of partially coherent, differentially coherent, and noncoherent communications. The generalized Marcum Q-function is defined by ...

An inverse function of an Abelian integral. Abelian functions have two variables and four periods, and can be defined by Theta(v,tau;q^'; ...

A recursive function devised by I. Takeuchi in 1978 (Knuth 1998). For integers x, y, and z, it is defined by (1) This can be described more simply by t(x,y,z)={y if x<=y; {z ...

The floor function |_x_|, also called the greatest integer function or integer value (Spanier and Oldham 1987), gives the largest integer less than or equal to x. The name ...

The nearest integer function, also called nint or the round function, is defined such that nint(x) is the integer closest to x. While the notation |_x] is sometimes used to ...

The totient function phi(n), also called Euler's totient function, is defined as the number of positive integers <=n that are relatively prime to (i.e., do not contain any ...

A function f:X->R is measurable if, for every real number a, the set {x in X:f(x)>a} is measurable. When X=R with Lebesgue measure, or more generally any Borel measure, then ...

The number of partitions of n with k or fewer addends, or equivalently, into partitions with no element greater than k. This function is denoted q(n,k) or q_k(n). (Note that ...

The j-function is the modular function defined by j(tau)=1728J(tau), (1) where tau is the half-period ratio, I[tau]>0, ...