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{\bf W. Zudilin}
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{\bf An Ap\'ery-like Difference Equation for Catalan's Constant}
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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 $\zeta(4)=\pi^4/90$.

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