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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 ...

A generalization of the complete beta function defined by B(z;a,b)=int_0^zu^(a-1)(1-u)^(b-1)du, (1) sometimes also denoted B_z(a,b). The so-called Chebyshev integral is given ...

An equation derived by Kronecker: where r(n) is the sum of squares function, zeta(z) is the Riemann zeta function, eta(z) is the Dirichlet eta function, Gamma(z) is the gamma ...

J_m(x)=(x^m)/(2^(m-1)sqrt(pi)Gamma(m+1/2))int_0^1cos(xt)(1-t^2)^(m-1/2)dt, where J_m(x) is a Bessel function of the first kind and Gamma(z) is the gamma function. Hankel's ...

y=delta^'(x-a), where delta(x) is the delta function.

Gamma functions of argument 2z can be expressed in terms of gamma functions of smaller arguments. From the definition of the beta function, ...

The elliptic lambda function lambda(tau) is a lambda-modular function defined on the upper half-plane by lambda(tau)=(theta_2^4(0,q))/(theta_3^4(0,q)), (1) where tau is the ...

A function of more than one variable.

A function f:A->B such that B is a set of numbers.

An apodization function similar to the Bartlett function.