Geodesic
Barnes' First Lemma and its Finite Analogue
Canadian mathematical bulletin, Tome 36 (1993) no. 3, pp. 273-282

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DOI

We give a parallel proof of Barnes' first lemma and of its finite analogue. In both cases we use the Mellin transform. In the classical case, the proof avoids the residue theorem. In the finite case the Gamma function is replaced by the Gaussian sum function and the beta function by the Jacobi sum function.
DOI : 10.4153/CMB-1993-039-1
Mots-clés : 33A15, 11L05, 20C99 
Helversen-Pasotto, Anna; Solé, Patrick. Barnes' First Lemma and its Finite Analogue. Canadian mathematical bulletin, Tome 36 (1993) no. 3, pp. 273-282. doi: 10.4153/CMB-1993-039-1
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     title = {Barnes' {First} {Lemma} and its {Finite} {Analogue}},
     journal = {Canadian mathematical bulletin},
     pages = {273--282},
     year = {1993},
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     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-1993-039-1/}
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