5 papers · 1 filter
A note on Clebsch-Gordan integral, Fourier-Legendre expansions and closed form for hypergeometric series
Marco Cantarini
In this paper we show that a closed form formula for the generalized Clebsch-Gordan integral and the Fourier-Legendre expansion theory allow to evaluate hypergeometric series invol…
A note on an average additive problem with prime numbers
Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini
We continue investigations on the average number of representations of a large positive integer as a sum of given powers of prime numbers. The average is taken over a short interva…
On the interplay between hypergeometric series, Fourier-Legendre expansions and Euler sums
Marco Cantarini, Jacopo D'Aurizio
In this work we continue the investigation about the interplay between hypergeometric functions and Fourier-Legendre () series expansions. In the section "Hypergeometr…
On the average number of representations of an integer as a sum of like prime powers
Marco Cantarini, Alessandro Gambini, Alessandro Zaccagnini
We investigate the average number of representations of a positive integer as the sum of perfect -th powers of primes. We extend recent results of Languasco and the last…
Explicit formula for the average of Goldbach and prime tuples representations
Marco Cantarini
Let be the Von Mangoldt function, let \[ r_{G}\left(n\right)=\underset{{\scriptstyle m_{1}+m_{2}=n}}{\sum_{m_{1},m_{2}\leq n}}Λ\left(m_{1}\right)Λ\left(m_{2}\righ…