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The spherical Bessel function of the second kind, denoted y_nu(z) or n_nu(z), is defined by y_nu(z)=sqrt(pi/(2z))Y_(nu+1/2)(z), (1) where Y_nu(z) is a Bessel function of the ...

Trigonometric functions of npi/11 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 11 is not a ...

Trigonometric functions of npi/13 for n an integer cannot be expressed in terms of sums, products, and finite root extractions on real rational numbers because 13 is not a ...

Trigonometric functions of npi/9 radians for n an integer not divisible by 3 (e.g., 40 degrees and 80 degrees) cannot be expressed in terms of sums, products, and finite root ...

Let F be the set of complex analytic functions f defined on an open region containing the set closure of the unit disk D={z:|z|<1} satisfying f(0)=0 and df/dz(0)=1. For each ...

The spherical Bessel function of the first kind, denoted j_nu(z), is defined by j_nu(z)=sqrt(pi/(2z))J_(nu+1/2)(z), (1) where J_nu(z) is a Bessel function of the first kind ...

A symmetric matrix is a square matrix that satisfies A^(T)=A, (1) where A^(T) denotes the transpose, so a_(ij)=a_(ji). This also implies A^(-1)A^(T)=I, (2) where I is the ...

The number of binary bits necessary to represent a number, given explicitly by BL(n) = 1+|_lgn_| (1) = [lg(n+1)], (2) where [x] is the ceiling function, |_x_| is the floor ...

The Epstein zeta function for a n×n matrix S of a positive definite real quadratic form and rho a complex variable with R[rho]>n/2 (where R[z] denotes the real part) is ...

A generalized continued fraction is an expression of the form b_0+(a_1)/(b_1+(a_2)/(b_2+(a_3)/(b_3+...))), (1) where the partial numerators a_1,a_2,... and partial ...