The most FUN Series I EVER Evaluated! An Analytic Number Theory EXTRAVAGANZA!

Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://www.amazon.com/shop/flammablemaths https://shop.spreadshirt.de/papaflammy Outtakes: https://youtu.be/Fjnkciqu-Cw Polygamma: https://www.youtube.com/watch?v=jHN-nnFbCcI Int Digamma: https://www.youtube.com/watch?v=SNUbR8lXD4M Catalan: https://www.youtube.com/watch?v=RapeuMPNnJU Geo Series: https://www.youtube.com/watch?v=F-w6RsRbLHQ pi^2/8: https://www.youtube.com/watch?v=y7vjpxz_ymI Leibniz Rule: https://www.youtube.com/watch?v=wkh1Y7R1sOw Today we are going to go extremely overboard! Let us use the Hurwitz Zeta funtction and the Trigamma function to solve this crazy series of 1/(4k+1)^2. This is just such a crazy beautiful and playful calculation extravaganza! At teh end we are going to end up with the trigamma function of 1/4 and Zeta(2,1/4) and catalan's constant! SO GOOD! 2nd Channel: https://www.youtube.com/channel/UCPctvztDTC3qYa2amc8eTrg -------------------------------------------------------------------------------- Wanna send me some stuff? lel: Postfach 60 06 03 14406 Potsdam Brandenburg Germany -------------------------------------------------------------------------------- My Website: https://www.papaflammy.engineer/ Flammy's subreddit: https://www.reddit.com/r/FlammyBois Twitter: https://twitter.com/FlammableMaths Facebook: https://www.facebook.com/flammablemaths/ Got some time to spare? Make sure to add captions to my videos! =) http://www.youtube.com/timedtext_cs_panel?c=UCtAIs1VCQrymlAnw3mGonhw&tab=2 Want to know more about me? Watch my QnA! =D https://youtu.be/IjCWSDBI9Zc