Today's calculation of Integral 548
Source: 2010 Ritsumeikan University entrance exam/Science
February 4, 2010
calculusintegrationtrigonometrycalculus computations
Problem Statement
For f(x)\equal{}e^{\frac{x}{2}}\cos \frac{x}{2}, evaluate \sum_{n\equal{}0}^{\infty} \int_{\minus{}\pi}^{\pi}f(x)f(x\minus{}2n\pi)dx\ (n\equal{}0,\ 1,\ 2,\ \cdots).