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We prove that the function Γ(x + a)Γ(x + b)/|Γ(x + c + iy)|2,a + b = 2c, and its q-analogue are of the form e−h(x,y) and h is completely… Click to show full abstract
We prove that the function Γ(x + a)Γ(x + b)/|Γ(x + c + iy)|2,a + b = 2c, and its q-analogue are of the form e−h(x,y) and h is completely monotonic in x. In particular both Γ(x + a)Γ(x + b)/|Γ(x + c + iy)|2 and Γq(x + a)Γq(x + b)/|Γq(x + c + iy)|2 are Laplace transforms of infinitely divisible distributions. We also extend Lerch’s inequality to the q-gamma function.
Keywords:
gamma functions;
functions complex;
complex arguments;
inequalities gamma;
gamma gamma
Journal Title: Analysis and Applications
Year Published: 2017
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Journal Title: Analysis and Applications
Year Published: 2017
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!