# Urukec

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# 20 Questions

 10 How to evaluate this integral $\int_{-\infty}^{+\infty}\frac{x^2e^x}{(1+e^x)^2}dx$? 5 How to calculate $|\operatorname {SL}_2(\mathbb Z/N\mathbb Z)|$? 4 How to verify this equation $\prod_{j=1}^\infty{1+\exp(i2^{-j}\omega)\over2}={1-\exp(i\omega)\over i\omega}$? 3 Poisson's summation formula 2 How to prove the convexity of the logrithmic gamma function?

# 389 Reputation

 +5 How to evaluate this integral $\int_{-\infty}^{+\infty}\frac{x^2e^x}{(1+e^x)^2}dx$? +10 How to prove the convexity of the logrithmic gamma function? +5 The trace of an integral equation? +10 Question about weight 2 Eisenstein series

 1 How to prove $g(z) = \frac {a \bar z + b } {c \bar z + d}$ is a bijective mapping of UHP to UHP? 1 Question about weight 2 Eisenstein series 1 Simplification of different base logarithms 1 Show that $p/q$ is the$[(1/2)(p+q-1)(p+q-2)+q]$th term of the series 1 $x,y$ related if and only if $x\cap\{{1,3,5\}}=y\cap\{{1,3,5\}}$.

# 44 Tags

 2 homework × 3 1 proof-strategy 1 complex-analysis × 6 1 rational-numbers 1 modular-forms × 3 1 logarithms 1 number-theory × 2 1 equivalence-relations 1 abstract-algebra 1 discrete-mathematics

# 8 Accounts

 Mathematics 389 rep 19 Science Fiction & Fantasy 128 rep 2 Cognitive Sciences 123 rep 2 Biology 121 rep 2 Physics 116 rep 2