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This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class $${\mathbb F}$$ F which contains Dirichlet ℒ -functions, ℒ -functions in… Click to show full abstract
This article investigates the algebraic differential independence concerning the Euler Γ-function and the function F in a certain class $${\mathbb F}$$ F which contains Dirichlet ℒ -functions, ℒ -functions in the extended Selberg class, or some periodic functions. We prove that the Euler Γ-function and the function F cannot satisfy any nontrivial algebraic differential equations whose coefficients are meromorphic functions ϕ with ρ ( ϕ ) < 1.
Keywords:
independence concerning;
euler function;
algebraic differential;
differential independence;
function
Journal Title: Acta Mathematica Scientia
Year Published: 2020
Link to full text (if available)
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Journal Title: Acta Mathematica Scientia
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!