Numerical computation of \prod_{n=1}^\infty (1 - tx^n)... The key lemma is a two-sidedbound on the Dedekind eta function at pure imaginary argument, \eta(iy), thatis sharp at the two endpoints y=0,\infty and is accurate to within 9.1%...
Numerical computation of ∞∏ (1 − txn) n=1... The key lemma is a two-sided bound on the Dedekind eta function at pure imaginary argument, η(iy), that is sharp at the two endpoints y = 0, ∞ and is accurate to within 9.1...
Heat kernel expansions on the integers... We show if L denotes the result of applying a finite number of Darboux transformations to L0 then the fundamental solution of ut = Lu is given by a finite sum of terms involving the Bessel function I of imaginary argument
Accurate approximations for the complex error function with small imaginary argumentIn this paper we present two efficient approximations for the complex error function w (z) with small imaginary argument Im [z] << 1 over the range 0 ≤ Re [z] ≤ 15 that is commonly considered difficult for highly accurate and rapid computation....
