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Slaying a Monster: Binet's Second Formula for Log Gamma

Train your Analytic Number Theory skills by trying out Brilliant! =D https://brilliant.org/FlammableMaths All the merch can be found over on https://stemerch.com/ :) Outtake:    • Видео   Arctan integral:    • Feynman would be proud. A Wonderful G...   Frullani + log integral:    • Frullani's Integral Identity   Gauss Digamma:    • Gauss' Representation for the Digamma...   Stirling:    • Factorial's Asymptotic Expansion - DE...   Leibniz Rule:    • The Leibniz rule for integrals: The D...   Mittag Leffler cotangent:    • The Cotangent's Series Expansion Deri...   Today we are going to derive an absolute Monster: Binet's Second Formula for Log Gamma (Natural Logarithm of the Gamma Function). For this we are going to manipulate the hell out of a parameterized integral. We use feynman integration, analytic number theory results and way more techniques to arrive at a crazy good asymptotic formula :) Enjoy! =D Help me create more free content! =) https://stemerch.com/   / mathable   Merch :v - https://papaflammy.myteespring.co/ https://www.amazon.com/shop/flammable... https://shop.spreadshirt.de/papaflammy Become a Member of the Flammily! :0    / @papaflammy69   2nd Channel:    / @npcooking69   -------------------------------------------------------------------------------- Wanna send me some stuff? lel: Postfach 11 15 06731 Bitterfeld-Wolfen Saxony-Anhalt Germany -------------------------------------------------------------------------------- Twitter:   / flammablemaths   Instagram:   / uncomfortably_cursed_mathmemes   Flammy's subreddit:   / flammybois   Facebook:   / flammablemaths   Want to know more about me? Watch my QnA! =D    • Question and Answer Time with Papa Fl...