Asymptotics and Super Asymptotics for Best Rational Approximation Error Norms to the Exponential Function (The ‘1/9’ Problem) by the Carathéodory-Fejér Method

Let E nbe the error norm of the best L ∞ rational approximation of degree n to the exponential function exp(-t) on [0,∞). Grounds are given for setting the conjectured limit E n / q n →2q 1/2 when n →∞, where q is the known constant ‘l/9’= 1/9.2890254919208189187554494359517450610316948677…, based on the singular values and functions of the relevant Henkel operator (Caratheodory-Fejer’s method).

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