
 
Benoit Cloitre
A Christmas formula for
Benoit Cloitre offers a Christmas formula for to us ! FormulaIf is Pocchammer's symbol, we obtain this general formula for , true for any :
ProofLet and . It is easy to check the WZtype relationship : Thus, using notations in [Wilf], we obtain Moreover, . The classical Euler's sum gives . Now, finally, from [Wilf], we obtain:
And so, as wanted.
References
[Wilf] H.S. Wilf, Accelerated series for universal constants, by the WZ method, Discrete Mathematics and Theorical Computer Science 3, 1999, 189192. Home page 