On the definition of the Euler Gamma function
Copyright policy )On the definition of the Euler Gamma function
We present a new definition of the Euler Gamma function. From the complex analysis and transalgebraic viewpoint, it is a natural characterization in the space of finite order meromorphic functions. We show how the classical theory and formulas develop naturally, and we discuss the relation with other definitions. We show in a companion article, that this definition generalizes to higher gamma functions and provides an unifying framework for their definition which is more natural than the usual Bohr–Mollerup or Lerch approaches.
- French National Centre for Scientific Research France
- Sorbonne University France
- Université Paris Cité France
- Institut de Mathématiques de Jussieu France
- Sorbonne Université France
Representations of entire functions of one complex variable by series and integrals, Mathematics - Complex Variables, Multiplicative and other generalized difference equations, entire function, infinite product, 30D30, Special classes of entire functions of one complex variable and growth estimates, 2010 Mathematics Subject Classification. Primary: 33B15. Secondary: 30D10, Euler gamma function, 30D15, Mathematics - Classical Analysis and ODEs, 33B15, 30D10, 30D15, 30D30, 39A20, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], Classical Analysis and ODEs (math.CA), FOS: Mathematics, meromorphic function, 39A20 Euler Gamma function, Complex Variables (math.CV), Gamma, beta and polygamma functions, Meromorphic functions of one complex variable (general theory)
Representations of entire functions of one complex variable by series and integrals, Mathematics - Complex Variables, Multiplicative and other generalized difference equations, entire function, infinite product, 30D30, Special classes of entire functions of one complex variable and growth estimates, 2010 Mathematics Subject Classification. Primary: 33B15. Secondary: 30D10, Euler gamma function, 30D15, Mathematics - Classical Analysis and ODEs, 33B15, 30D10, 30D15, 30D30, 39A20, [MATH.MATH-CV] Mathematics [math]/Complex Variables [math.CV], Classical Analysis and ODEs (math.CA), FOS: Mathematics, meromorphic function, 39A20 Euler Gamma function, Complex Variables (math.CV), Gamma, beta and polygamma functions, Meromorphic functions of one complex variable (general theory)
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