Departmental Bulletin Paper CONVOLUTION IDENTITIES FOR CAUCHY NUMBERS OF THE SECOND KIND

Komatsu, Takao

69 ( 1 )  , pp.125 - 144 , 2015-06-09 , Faculty of Mathematics, Kyushu University
ISSN:1340-6116
NCID:AA10994346
Description
Let ĉ_n be the nth Cauchy number of the second kind, defined by the generating function x/(1 + x) ln(1 + x) = Σ^^∞__<n=0> ĉ_nx^n/n!. We obtain explicit expressions for (ĉ_l + ĉ_m)^n := Σ^^∞__<j=0> (nj)ĉ_<l+j>ĉ<m+n−j> with arbitrary fixed integers l, m ≥ 0. The corresponding expression for Bernoulli numbers has been studied by Agoh and Dilcher, and that for Cauchy numbers of the first kind by the author.

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