On differential independence of $\boldsymbol{\zeta }$ and ${\boldsymbol{\varGamma }}$
Volume 124 / 2020
Annales Polonici Mathematici 124 (2020), 151-159
MSC: Primary 11M06, 33B15; Secondary 26B05, 30D30, 34M15.
DOI: 10.4064/ap190621-17-9
Published online: 9 January 2020
Abstract
We prove that $\boldsymbol {\zeta }$ and $\boldsymbol {\Gamma }$ cannot satisfy any differential equation generated by a function from a family of functions continuous in $\boldsymbol {\zeta },\boldsymbol {\zeta }’,\ldots ,\boldsymbol {\zeta }^{(m)}$ and polynomial in $\boldsymbol {\Gamma },\boldsymbol {\Gamma }’,\ldots ,\boldsymbol {\Gamma }^{(n)}$.
