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The canonical bundle is a holomorphic line bundle on a complex manifold which is determined by its complex structure. On a coordinate chart (z_1,...z_n), it is spanned by the ...

Orthogonal polynomials associated with weighting function w(x) = pi^(-1/2)kexp(-k^2ln^2x) (1) = pi^(-1/2)kx^(-k^2lnx) (2) for x in (0,infty) and k>0. Defining ...

A universal differential equation (UDE) is a nontrivial differential-algebraic equation with the property that its solutions approximate to arbitrary accuracy any continuous ...

The d-analog of a complex number s is defined as [s]_d=1-(2^d)/(s^d) (1) (Flajolet et al. 1995). For integer n, [2]!=1 and [n]_d! = [3][4]...[n] (2) = ...

where _2F_1(a,b;c;z) is a hypergeometric function and _3F_2(a,b,c;d,e;z) is a generalized hypergeometric function.

The tangential circle of a reference triangle is the circumcircle of the tangential triangle. Its center is Kimberling center X_(26), which has center function ...

The theta series of a lattice is the generating function for the number of vectors with norm n in the lattice. Theta series for a number of lattices are implemented in the ...

The q-hypergeometric function identity _rphi_s^'[a,qsqrt(a),-qsqrt(a),1/b,1/c,1/d,1/e,1/f; sqrt(a),-sqrt(a),abq,acq,adq,aeq,afq] ...

The distribution with probability density function and distribution function P(x) = (ab^a)/(x^(a+1)) (1) D(x) = 1-(b/x)^a (2) defined over the interval x>=b. It is ...

The integral transform defined by (Kphi)(x)=int_0^inftyG_(pq)^(mn)(xt|(a_p); (b_q))phi(t)dt, where G_(pq)^(mn) is a Meijer G-function. Note the lower limit of 0, not -infty ...