On the Asymptotic Expansions of the (<i>p</i>,<i>k</i>)-Analogues of the Gamma Function and Associated Functions

On the Asymptotic Expansions of the (<i>p</i>,<i>k</i>)-Analogues of the Gamma Function and Associated Functions

General asymptotic expansion of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow&g...

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Bibliographic Details
Main Author:	Tomislav Burić
Format:	Article
Language:	English
Published:	MDPI AG 2025-01-01
Series:	Axioms
Subjects:	asymptotic expansion gamma function (<i>p</i>,<i>k</i>)-gamma function quotient of gamma functions <i>k</i>-Pochhammer symbol
Online Access:	https://www.mdpi.com/2075-1680/14/1/55
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Summary:	General asymptotic expansion of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>-gamma function is obtained and various approaches to this expansion are studied. The numerical precision of the derived asymptotic formulas is shown and compared. Results are applied to the analogues of digamma and polygamma functions, and asymptotic expansion of the quotient of two <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>(</mo><mi>p</mi><mo>,</mo><mi>k</mi><mo>)</mo></mrow></semantics></math></inline-formula>-gamma functions is also derived and analyzed. Various examples and application to the <i>k</i>-Pochhammer symbol are presented.
ISSN:	2075-1680