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Padé approximant related to asymptotics for the gamma function
1Department of Mathematics, East China Normal University, 500 Dongchuan Road, Shanghai, 200241 People's Republic of China.
Journal of Inequalities and Applications
|March 18, 2017
Summary
Researchers used Padé approximation to find coefficients for the gamma function, establishing new bounds. This mathematical method enhances understanding of the gamma function
Area of Science:
- Mathematics
- Mathematical Analysis
Background:
- The gamma function is a fundamental concept in mathematical analysis, extending the factorial function to complex and real numbers.
- Understanding and accurately bounding the gamma function are crucial for various fields, including statistics, physics, and engineering.
Purpose of the Study:
- To determine specific coefficients using the Padé approximation method.
- To establish novel inequalities and bounds for the gamma function based on these coefficients.
Main Methods:
- The study employs the Padé approximation method to derive precise coefficients.
- These coefficients are then utilized to construct new analytical expressions.
Main Results:
- The coefficients [Formula: see text] and [Formula: see text] were successfully determined for any integer [Formula: see text].
- New, rigorously derived bounds for the gamma function were established.
Conclusions:
- The Padé approximation method provides an effective tool for analyzing the gamma function.
- The newly established bounds offer improved accuracy and utility in mathematical applications.
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