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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 values, or proofs of some of the formulas.

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International audience Random Apollonian networks have been recently introduced for representing real graphs. In this paper we study a modified version: random Apollonian network structures (RANS), which preserve the interesting properties of real graphs and can be handled with powerful tools of random generation. We exhibit a bijection between RANS and ternary trees, that transforms the degree of nodes in a RANS into the size of particular subtrees. The distribution of degrees in RANS can thus be analysed within a bivariate Boltzmann model for the generation of random trees, and we show that it has a Catalan form which reduces to a power law with an exponential cutoff: $α ^k k^{-3/2}$, with $α = 8/9$. We also show analogous distributions for the degree in RANS of higher dimension, related to trees of higher arity.