Sir cu integrale

[c.adryan]

Fie \( 0<a<b \) si \( (x_n)_n_\geq_0,\ (y_n)_n_\geq_0 \) doua siruri cu \( x_0=a,\ y_0=0 \)
\( x_{n+1}=\int_{x_n}^{y_n} e^{-\frac{a^2}{t^2}} dt \),
\( y_{n+1}=\int_{y_n}^{x_n} e^{-\frac{b^2}{t^2}} dt \).
Demonstrati ca cele doua siruri sunt convergente si aflati limita lor.