The Euler–Mascheroni constant is defined as the limiting difference between the harmonic series and the natural logarithmpic.twitter.com/9oOFgh3C4J
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Same with Catalan's constant G. We know nothing about it. It also appears in many integrals (e.g. with cotangent)pic.twitter.com/jkTTSwWbAJ
This is actually a rather deep statement, as the EM constant appears all the time in QFT renormalization
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G? Nah. It's β(2). As you know β(1) = π/4. Turns out β(3) = π³/32. And β(5) = 5π⁵/1536. All the odd beta's are known and the even beta's are mysterious. Exactly opposite of Riemann zeta function! ζ(2) = π²/6 and ζ(4) = π⁴/90 etc but the odd zeta's like ζ(3) are mysterious!!pic.twitter.com/PdKC5tN2Hv
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