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A very large number defined in terms of circle notation by Steinhaus (1983) as .

P_n(cosalpha)=(sqrt(2))/piint_0^alpha(cos[(n+1/2)phi])/(sqrt(cosphi-cosalpha))dphi, where P_n(x) is a Legendre polynomial.

The integral transform defined by g(x)=int_1^inftyt^(1/4-nu/2)(t-1)^(1/4-nu/2)P_(-1/2+ix)^(nu-1/2)(2t-1)f(t)dt (Samko et al. 1993, p. 761) or ...

For x>0, J_0(x) = 2/piint_0^inftysin(xcosht)dt (1) Y_0(x) = -2/piint_0^inftycos(xcosht)dt, (2) where J_0(x) is a zeroth order Bessel function of the first kind and Y_0(x) is ...

(1) where H_n(x) is a Hermite polynomial (Watson 1933; Erdélyi 1938; Szegö 1975, p. 380). The generating function ...

The Meijer G-function is a very general function which reduces to simpler special functions in many common cases. The Meijer G-function is defined by (1) where Gamma(s) is ...

The integral transform (Kf)(x)=int_0^inftysqrt(xt)K_nu(xt)f(t)dt, where K_nu(x) is a modified Bessel function of the second kind. Note the lower limit of 0, not -infty as ...

A modification of Legendre's formula for the prime counting function pi(x). It starts with |_x_| = (1) where |_x_| is the floor function, P_2(x,a) is the number of integers ...

Meißner (1911) showed how to modify the Reuleaux tetrahedron (which is not a solid of constant width) to form a surface of constant width by replacing three of its edge arcs ...

The hypergeometric orthogonal polynomials defined by P_n^((lambda))(x;phi)=((2lambda)_n)/(n!)e^(inphi)_2F_1(-n,lambda+ix;2lambda;1-e^(-2iphi)), (1) where (x)_n is the ...