page_title: Hadamard's gamma function
hierarchical_section_title: Hadamard's gamma function
caption_attribution_description: English: Hadamard's Gamma function plotted over part of the real axis. Unlike the classic Gamma function it is holomorphic, there are no poles. Created via Sage Cell Server with plot(diff(ln(gamma(1/2-x/2)/gamma(1-x/2)), x)/gamma(1-x), x, -5, 5)
context_page_description: In mathematics, Hadamard's gamma function, named after Jacques Hadamard, is an extension of the factorial function, different from the classical gamma function. This function, with its argument shifted down by 1, interpolates the factorial and extends it to real and complex numbers in a different way than Euler's gamma function. It is defined as:
  where Γ(x) denotes the classical gamma function. If n is a positive integer, then:
context_section_description: In mathematics, Hadamard's gamma function, named after Jacques Hadamard, is an extension of the factorial function, different from the classical gamma function. This function, with its argument shifted down by 1, interpolates the factorial and extends it to real and complex numbers in a different way than Euler's gamma function. It is defined as:
  where Γ(x) denotes the classical gamma function. If n is a positive integer, then:
caption: Hadamard's gamma function plotted over part of the real axis. Unlike the classical gamma function, it is holomorphic; there are no poles.
exif: {}