Daniel Ángeles

Posting about Theory of Functions and Fourier Series

[Daniel Ángeles @Javier_DanielAR]

Take a look at this weird integral. #Mathchallenge

[Daniel Ángeles @Javier_DanielAR]

@chris_juravich Good morning !

[Daniel Ángeles @Javier_DanielAR]

Here's a nice Mellin transform problem for this weekend, give it a try! #mathfun

[Daniel Ángeles @Javier_DanielAR]

@chris_juravich Check this thread for hints on how to solve this puzzle which is basically the way this Mellin transform was calculated before Cauchy 3/3

[Daniel Ángeles @Javier_DanielAR]

#math

[Daniel Ángeles @Javier_DanielAR]

@chris_juravich and in doing so, you're implicitly using the definition of a contour integral. This is the reason why the basic scaling property for the Mellin transform works only for positive real constants 2/3

[⛵️ @zzbar]

@Javier_DanielAR Solved these two using Ledgendre polynomials and some basic hypergeometric recursion formula.

[Daniel Ángeles @Javier_DanielAR]

@zzbar Great!, many thanks for your answer

[Daniel Ángeles @Javier_DanielAR]

#mathcallenge

[Daniel Ángeles @Javier_DanielAR]

#math

[Daniel Ángeles @Javier_DanielAR]

#math

[Daniel Ángeles @Javier_DanielAR]

@psicoalfanista What I can say for now, is that the hint will be related to the parameter s….

[Daniel Ángeles @Javier_DanielAR]

@psicoalfanista and to prove that analytic functions have a Taylor series expansion, we use the Cauchy integral formula. Tomorrow I will give a series of hints for this problem 2/2

[Daniel Ángeles @Javier_DanielAR]

Take a look at this amazing answer. Professor @SrinivasR1729 masterfully solved this puzzle using clever elliptic integration techniques

[𝐒𝐫𝐢𝐧𝐢𝐯𝐚𝐬𝐚 𝐑𝐚𝐠𝐡𝐚𝐯𝐚 ζ(1/2 + i σₙ )=0 @SrinivasR1729]

Here is my detailed solution to this beautiful arcsine-lemniscate integral.

[Daniel Ángeles @Javier_DanielAR]

@charrlie3045 Elliptic integrals of the first and second kinds are invariant under a sign change of the modulus, that's why the answer is basically the same!

[Daniel Ángeles @Javier_DanielAR]

@charrlie3045 Many thanks for your clever answer! Sorry for correcting the signs after you had posted your solution

[Toluwanimicharles @charrlie3045]

@Javier_DanielAR

[Daniel Ángeles @Javier_DanielAR]

@chris_juravich Hi, the problems are spread out all over my account, I'll try to organize them into one thread

[Daniel Ángeles @Javier_DanielAR]

#mathfun