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For a positive integer n, (2pi)^((n-1)/2)n^(1/2-nz)Gamma(nz)=product_(k=0)^(n-1)Gamma(z+k/n),

The second-order ordinary differential equation (d^2y)/(dx^2)-2x(dy)/(dx)+lambday=0. (1) This differential equation has an irregular singularity at infty. It can be solved ...

A univariate distribution proportional to the F-distribution. If the vector d is Gaussian multivariate-distributed with zero mean and unit covariance matrix N_p(0,I) and M is ...

A relation expressing a sum potentially involving binomial coefficients, factorials, rational functions, and power functions in terms of a simple result. Thanks to results by ...

Let X be an infinite set of urelements, and let V(^*X) be an enlargement of the superstructure V(X). Let A,B in V(X) be finitary algebras with finitely many operations, and ...

The complex second-order ordinary differential equation x^2y^('')+xy^'-(ix^2+nu^2)y=0 (1) (Abramowitz and Stegun 1972, p. 379; Zwillinger 1997, p. 123), whose solutions can ...

Given a sum and a set of weights, find the weights which were used to generate the sum. The values of the weights are then encrypted in the sum. This system relies on the ...

A procedure for determining the behavior of an nth order ordinary differential equation at a removable singularity without actually solving the equation. Consider ...

Leakage, more explicitly called spectral leakage, is a smearing of power across a frequency spectrum that occurs when the signal being measured is not periodic in the sample ...

A field which is complete with respect to a discrete valuation is called a local field if its field of residue classes is finite. The Hasse principle is one of the chief ...