Product Form of Euler’s Limit Formula for the Gamma Function
This note is a continuation of last one. By the definition of , for , we can rewrite it in the following form,
asymptotic analysis
Asymptotic Expansion of Bessel Functions For Large Argument
This note is based on Appendix B.7 and B.8 of (Grafakos, 2008). First, we show that Bessel function can be written into the following form
Euler’s Limit Formula for the Gamma Function
This note is based on the Appendix A.7 of (Grafakos, 2008). The gamma function is defined by the integral . For integer this defines the factorial up to . ...
Proof of Stirling’s Formula
Stirling’s formula is very useful in all kinds of asymptotic analysis. Here we present one of many proofs.