81 citations · 304 across the 72 of their papers we have counts for
77 papers
Dubious Identities: A Visit to the Borwein Zoo
Zachary P. Bradshaw, Christophe Vignat
We contribute to the zoo of dubious identities established by J.M. and P.B. Borwein in their 1992 paper, "Strange Series and High Precision Fraud" with five new entries, each of a…
Curious multisection identities by index factorization
C. Vignat, M. Milgram
This manuscript introduces a general multisection identity expressed equivalently in terms of infinite double products and/or infinite double series, from which several new product…
Probabilistic aspects of Jacobi theta functions
Paavo Salminen, Christophe Vignat
In this note we deduce well known modular identities for Jacobi theta functions using the spectral representations associated with the real valued Brownian motion taking values on…
unexpected logarithmic identities and other surprises
C. Vignat
This is a journey through integrals of involutions and surprising consequences of the Lagrange inversion theorem. On the way, we meet unexpected logarithmic identities, hypergeomet…
An Operational Calculus Generalization of Ramanujan's Master Theorem
Zachary P. Bradshaw, Christophe Vignat
We give a formal extension of Ramanujan's master theorem using operational methods. The resulting identity transforms the computation of a product of integrals on the half-line to…
Dirichlet Series Under Standard Convolutions: Variations on Ramanujan's Identity for Odd Zeta Values
Parth Chavan, Sarth Chavan, Christophe Vignat +1
Inspired by a famous identity of Ramanujan, we propose a general formula linearizing the convolution of Dirichlet series as the sum of Dirichlet series with modified weights; its s…