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A prime p for which 1/p has a maximal period decimal expansion of p-1 digits. Full reptend primes are sometimes also called long primes (Conway and Guy 1996, pp. 157-163 and ...

tau is the ratio tau=omega_2/omega_1 of the two half-periods omega_1 and omega_2 of an elliptic function (Whittaker and Watson 1990, pp. 463 and 473) defined such that the ...

Solving the nome q for the parameter m gives m(q) = (theta_2^4(q))/(theta_3^4(q)) (1) = (16eta^8(1/2tau)eta^(16)(2tau))/(eta^(24)(tau)), (2) where theta_i(q)=theta_i(0,q) is ...

A linear transformation of period two. Since a linear transformation has the form, lambda^'=(alphalambda+beta)/(gammalambda+delta), (1) applying the transformation a second ...

The Kermack-McKendrick model is an SIR model for the number of people infected with a contagious illness in a closed population over time. It was proposed to explain the ...

Let omega_1 and omega_2 be periods of a doubly periodic function, with tau=omega_2/omega_1 the half-period ratio a number with I[tau]!=0. Then Klein's absolute invariant ...

A phenomenon in which a system being forced at an irrational period undergoes rational, periodic motion which persists for a finite range of forcing values. It may occur for ...

In 1979, Conway and Norton discovered an unexpected intimate connection between the monster group M and the j-function. The Fourier expansion of j(tau) is given by (1) (OEIS ...

Given a Jacobi theta function, the nome is defined as q(k) = e^(piitau) (1) = e^(-piK^'(k)/K(k)) (2) = e^(-piK(sqrt(1-k^2))/K(k)) (3) (Borwein and Borwein 1987, pp. 41, 109 ...

A periodic continued fraction is a continued fraction (generally a regular continued fraction) whose terms eventually repeat from some point onwards. The minimal number of ...