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The nontrivial zeros of the Riemann zeta function correspond to the eigenvalues of some Hermitian operator (Derbyshire 2004, pp. 277-278).

Special functions which arise as solutions to second order ordinary differential equations are commonly said to be "of the first kind" if they are nonsingular at the origin, ...

A sequent is an expression Gamma|-Lambda, where Gamma and Lambda are (possibly empty) sequences of formulas. Here, Gamma is called the antecedent and Lambda is called the ...

The two-dimensional map x_(n+1) = [x_n+nu(1+muy_n)+epsilonnumucos(2pix_n)] (mod 1) (1) y_(n+1) = e^(-Gamma)[y_n+epsiloncos(2pix_n)], (2) where mu=(1-e^(-Gamma))/Gamma (3) ...

A Taylor series is a series expansion of a function about a point. A one-dimensional Taylor series is an expansion of a real function f(x) about a point x=a is given by (1) ...

Every nonconstant entire function attains every complex value with at most one exception (Henrici 1988, p. 216; Apostol 1997). Furthermore, every analytic function assumes ...

Krall and Fink (1949) defined the Bessel polynomials as the function y_n(x) = sum_(k=0)^(n)((n+k)!)/((n-k)!k!)(x/2)^k (1) = sqrt(2/(pix))e^(1/x)K_(-n-1/2)(1/x), (2) where ...

A method for computing the prime counting function. Define the function T_k(x,a)=(-1)^(beta_0+beta_1+...+beta_(a-1))|_x/(p_1^(beta_0)p_2^(beta_1)...p_a^(beta_(a-1)))_|, (1) ...

The sawtooth wave, called the "castle rim function" by Trott (2004, p. 228), is the periodic function given by S(x)=Afrac(x/T+phi), (1) where frac(x) is the fractional part ...

The Gram series is an approximation to the prime counting function given by G(x)=1+sum_(k=1)^infty((lnx)^k)/(kk!zeta(k+1)), (1) where zeta(z) is the Riemann zeta function ...