Is there any infinite series representation of the sine integral?
It is defined as $$\displaystyle \int\ \frac{\sin(x)}{x}\ dx$$
2026-04-13 04:26:13.1776054373
Is there any infinite series representation of the sine integral?
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$$\int \frac{\sin{x}}{x}dx=\int\frac{\sum_{k=0}^{\infty}(-1)^k\frac{x^{2k+1}}{(2k+1)!}}{x}dx=\int\sum_{k=0}^{\infty}(-1)^k\frac{x^{2k}}{(2k+1)!}=\sum_{k=0}^{\infty}(-1)^k \frac{x^{2k+1}}{(2k+1)!\cdot (2k+1)}$$