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The Euler-Mascheroni constant gamma=0.577215664901532860606512090082402431042... (OEIS A001620) was calculated to 16 digits by Euler in 1781 and to 32 decimal places by ...

The fast Fourier transform (FFT) is a discrete Fourier transform algorithm which reduces the number of computations needed for N points from 2N^2 to 2NlgN, where lg is the ...

In three dimensions, there are three classes of constant curvature geometries. All are based on the first four of Euclid's postulates, but each uses its own version of the ...

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

A general quadratic Diophantine equation in two variables x and y is given by ax^2+cy^2=k, (1) where a, c, and k are specified (positive or negative) integers and x and y are ...

If (1-z)^(a+b-c)_2F_1(2a,2b;2c;z)=sum_(n=0)^inftya_nz^n, then where (a)_n is a Pochhammer symbol and _2F_1(a,b;c;z) is a hypergeometric function.

A hypergeometric function in which one parameter changes by +1 or -1 is said to be contiguous. There are 26 functions contiguous to _2F_1(a,b;c;x) taking one pair at a time. ...

A transformation of a hypergeometric function,

An identity which relates hypergeometric functions,

The word quadrature has (at least) three incompatible meanings. Integration by quadrature either means solving an integral analytically (i.e., symbolically in terms of known ...