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 126 Is there a symbol for “taking a derivative of something”? 91 Can sum of a rational number and its reciprocal be an integer? 41 Unexpected examples of natural logarithm 25 Find the probability that the thirteenth spade will appear before the thirteenth diamond? 19 An astounding identity: $\int_0^{\pi/2}\ln\lvert\sin(mx)\rvert\cdot \ln\lvert\sin(nx)\rvert\, dx$

### Reputation (23,021)

 +5 Asymptotic behavior of $x_{n+1}=x_n+\frac{1}{x_n}, \space\space\space x_0=1$ +10 An interesting twist on Cauchy's functional equation +5 Strange functional equation: $f(x)+f(\cos(x))=x$ +10 What are some standard methods for solving functional equations?

### Questions (195)

 203 “Integral Milking” 80 Do numbers get worse than transcendental? 60 Find three non-constant, pairwise unequal functions $f,g,h:\mathbb R\to \mathbb R$… 49 What numbers can be created by $1-x^2$ and $x/2$? 33 Painting the plane, and finding points one unit apart

### Tags (284)

 368 calculus × 82 134 number-theory × 24 212 integration × 76 129 definite-integrals × 54 204 algebra-precalculus × 42 126 notation × 3 200 sequences-and-series × 80 113 elementary-number-theory × 16 158 derivatives × 20 105 real-analysis × 41

### Accounts (16)

 Mathematics 23,021 rep 842112 Puzzling 946 rep 121 Area 51 426 rep 9 Philosophy 163 rep 16 Economics 156 rep 3