The consideration of tensor products of $0$-Hecke algebra modules leads to natural analogs of the Bessel $J$-functions in the algebra of noncommutative symmetric functions. This provides a simple explanation of various combinatorial properties of Bessel functions.

MSC Classifications:

05E05, 16W30, 05A15 show english descriptions Symmetric functions and generalizations
Coalgebras, bialgebras, Hopf algebras (See also 16S40, 57T05); rings, modules, etc. on which these act
Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx] 05E05 - Symmetric functions and generalizations
16W30 - Coalgebras, bialgebras, Hopf algebras (See also 16S40, 57T05); rings, modules, etc. on which these act
05A15 - Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]

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