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Define q=e^(2piitau) (cf. the usual nome), where tau is in the upper half-plane. Then the modular discriminant is defined by ...

product_(k=1)^(infty)(1-x^k) = sum_(k=-infty)^(infty)(-1)^kx^(k(3k+1)/2) (1) = 1+sum_(k=1)^(infty)(-1)^k[x^(k(3k-1)/2)+x^(k(3k+1)/2)] (2) = (x)_infty (3) = ...

There are a number of functions in various branches of mathematics known as Riemann functions. Examples include the Riemann P-series, Riemann-Siegel functions, Riemann theta ...

The tangent numbers, also called a zag number, and given by T_n=(2^(2n)(2^(2n)-1)|B_(2n)|)/(2n), (1) where B_n is a Bernoulli number, are numbers that can be defined either ...

A temporal point process is a random process whose realizations consist of the times {tau_j}_(j in J) of isolated events. Note that in some literature, the values tau_j are ...

sum_(n=0)^(infty)[(q)_infty-(q)_n] = g(q)+(q)_inftysum_(k=1)^(infty)(q^k)/(1-q^k) (1) = g(q)+(q)_inftyL(q) (2) = g(q)+(q)_infty(psi_q(1)+ln(1-q))/(lnq) (3) = ...

Analysis

A Bessel function of the second kind Y_n(x) (e.g, Gradshteyn and Ryzhik 2000, p. 703, eqn. 6.649.1), sometimes also denoted N_n(x) (e.g, Gradshteyn and Ryzhik 2000, p. 657, ...

The Egyptian Mathematical Leather Roll (EMLR), dates to the Middle Kingdom, and was purchased in Egypt in 1858 by Henry Rhind, near the time when the Rhind papyrus was ...

For s>1, the Riemann zeta function is given by zeta(s) = sum_(n=1)^(infty)1/(n^s) (1) = product_(k=1)^(infty)1/(1-1/(p_k^s)), (2) where p_k is the kth prime. This is Euler's ...