Marc Mezzarobba

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We describe the main features of the Dynamic Dictionary of Mathematical Functions (version 1.5). It is a website consisting of interactive tables of mathematical formulas on elementary and special functions. The formulas are automatically generated by computer algebra routines. The user can ask for more terms of the expansions, more digits of the numerical(More)
We describe an algorithm that takes as input a complex sequence (un) given by a linear recurrence relation with polynomial coe cients along with initial values, and outputs a simple explicit upper bound (vn) such that |un| ≤ vn for all n. Generically, the bound is tight, in the sense that its asymptotic behaviour matches that of un. We discuss applications(More)
We introduce a software-oriented algorithm that allows one to quickly compare a binary64 floating-point (FP) number and a decimal64 FP number, assuming the "binary encoding" of the decimal formats specified by the IEEE 754-2008 standard for FP arithmetic is used. It is a two-step algorithm: a first pass, based on the exponents only, makes it possible to(More)
We introduce an algorithm to compare a binary floating-point (FP) number and a decimal FP number, assuming the “binary encoding” of the decimal formats is used, and with a special emphasis on the basic interchange formats specified by the IEEE 754-2008 standard for FP arithmetic. It is a two-step algorithm: a first pass, based on the exponents only, quickly(More)
The series expansion at the origin of the Airy function Ai(x) is alternating and hence problematic to evaluate for x > 0 due to cancellation. Based on a method recently proposed by Gawronski, Müller, and Rein hard, we exhibit two functions F and G, both with nonnegative Taylor expansions at the origin, such that Ai(x) = G(x)/F(x). The sums are(More)
Nous exposons un ensemble de méthodes qui permettent d’évaluer « en forme close », c’est-à-dire sans signe P , de vastes classes de sommes discrètes, et de trouver des démonstrations faciles à vérifier des identités obtenues. Les principaux ingrédients sont l’algorithme de Gosper, qui traite le cas des sommes « indéfinies » Pn t(k), celui de Zeilberger, qui(More)