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Results tagged with real-analysis
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user 122762
Real-valued functions of real variable, analytic properties of functions and sequences, limits, continuity, smoothness of these.
6
votes
"Simple" integral equation
Alternative simple proof - integration by parts:
$$
\int_0^{1-a}\frac{H(z)}{1-z}dz=\int_0^{1-a}\frac1{(1-z)^2}\int_z^1\frac{2\zeta}{1+\zeta}H(\zeta^2)d\zeta=
$$
$$
\frac1{1-z}\int_z^1\frac{2\zeta}{1 …
- 283
11
votes
3
answers
1k
views
"Simple" integral equation
Let $H(z)$ be a continuous solution of the problem
$$
H(z)=\frac1{1-z}\int_z^1 \frac{2\zeta}{1+\zeta} H(\zeta^2)\,d\zeta,\ \ \ z\in[0,1);\ \ \ H(1)=1.
$$
Is it true that $H(0)=1-\ln2$? The question i …
- 283