A computer proof of Turán's inequality.
A proof of a conjecture of Knuth.
About a new kind of Ramanujan-type series.
Accelerated series for universal constants, by the WZ method.
An Apéry-like difference equation for Catalan's constant.
Analytic and combinatoric aspects of Hurwitz polyzêtas
In this work, a symbolic encoding of generalized Di-richlet generating series is found thanks to combinatorial techniques of noncommutative rational power series. This enables to explicit periodic generalized Dirichlet generating series – particularly the coloured polyzêtas – as linear combinations of Hurwitz polyzêtas. Moreover, the noncommutative version of the convolution theorem gives easily rise to an integral representation of Hurwitz polyzêtas. This representation enables us to build the...
Apéry's double sum is plain sailing indeed.