Fixed-lower-limit sine-integral expansion

For

si (x) = \int_{1}^{\infty} \frac{s i n ( x t )}{t} d t,

repeated integration by parts gives

si (x) \sim cos x \sum_{n \geq 0} (- 1)^{n} (2 n)! x^{- 2 n - 1} + sin x \sum_{n \geq 0} (- 1)^{n} (2 n + 1)! x^{- 2 n - 2} .

 Ancestors (6)