An Apéry-like Difference Equation for Catalan's Constant

W. Zudilin
2003 Electronic Journal of Combinatorics  
Applying Zeilberger's algorithm of creative telescoping to a family of certain very-well-poised hypergeometric series involving linear forms in Catalan's constant with rational coefficients, we obtain a second-order difference equation for these forms and their coefficients. As a consequence we derive a new way of fast calculation of Catalan's constant as well as a new continued-fraction expansion for it. Similar arguments are put forward to deduce a second-order difference equation and a new continued fraction for $\zeta(4)=\pi^4/90$.
doi:10.37236/1707 fatcat:ommpqyr6mbhg7hygboyxipvgwu