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The cosine function cosx is one of the basic functions encountered in trigonometry (the others being the cosecant, cotangent, secant, sine, and tangent). Let theta be an ...

The application of an apodization function.

A space-filling function.

Einstein summation is a notational convention for simplifying expressions including summations of vectors, matrices, and general tensors. There are essentially three rules of ...

The eight Gell-Mann matrices lambda_i, i=1,...,8, are an example of the set of generators of the Lie algebra associated to the special unitary group SU(3). Explicitly, these ...

When the elliptic modulus k has a singular value, the complete elliptic integrals may be computed in analytic form in terms of gamma functions. Abel (quoted in Whittaker and ...

A transformation of a hypergeometric function,

where _8phi_7 is a q-hypergeometric function.

_2phi_1(a,q^(-n);c;q,q)=(a^n(c/a,q)_n)/((a;q)_n), where _2phi_1(a,b;c;q,z) is a q-hypergeometric function.

Solutions to the associated Laguerre differential equation with nu!=0 and k an integer are called associated Laguerre polynomials L_n^k(x) (Arfken 1985, p. 726) or, in older ...