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Jacobi-Gauss quadrature, also called Jacobi quadrature or Mehler quadrature, is a Gaussian quadrature over the interval [-1,1] with weighting function ...

The Legendre transform of a sequence {c_k} is the sequence {a_k} with terms given by a_n = sum_(k=0)^(n)(n; k)(n+k; k)c_k (1) = sum_(k=0)^(n)(2k; k)(n+k; n-k)c_k, (2) where ...

Long division is an algorithm for dividing two numbers, obtaining the quotient one digit at a time. The example above shows how the division of 123456/17 is performed to ...

Polynomials m_k(x;beta,c) which form the Sheffer sequence for g(t) = ((1-c)/(1-ce^t))^beta (1) f(t) = (1-e^t)/(c^(-1)-e^t) (2) and have generating function ...

The metagyrate diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(78). The unit metagyrate diminished rhombicosidodecahedron has volume ...

A map projection given by the following transformation, x = lambda-lambda_0 (1) y = 5/4ln[tan(1/4pi+2/5phi)] (2) = 5/4sinh^(-1)[tan(4/5phi)]. (3) Here, x and y are the plane ...

The parabiaugmented dodecahedron is a convex equilateral solid that is Johnson solid J_(60). The unit parabiaugmented dodecahedron has volume V=1/6(25+11sqrt(5)) (1) and Dehn ...

The parabididiminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(820). The unit parabididiminished rhombicosidodecahedron ...

The paragyrate diminished rhombicosidodecahedron is a convex equilateral solid that is Johnson solid J_(77). The unit paragyrate diminished rhombicosidodecahedron has volume ...

The pentagonal gyrobicupola is a convex equilateral solid that is Johnson solid J_(31). The unit pentagonal gyrobicupola has volume V=1/3(5+4sqrt(5)) (1) and Dehn invariant D ...