\[\operatorname{kei}_{n}x=-\tfrac{1}{2}(\tfrac{1}{2}x)^{-n}\sum_{k=0}^{n-1}\frac%
{(n-k-1)!}{k!}\sin\left(\tfrac{3}{4}n\pi+\tfrac{1}{2}k\pi\right)(\tfrac{1}{4}x%
^{2})^{k}-\ln\left(\tfrac{1}{2}x\right)\operatorname{bei}_{n}x-\tfrac{1}{4}\pi%
\operatorname{ber}_{n}x+\tfrac{1}{2}(\tfrac{1}{2}x)^{n}\sum_{k=0}^{\infty}%
\frac{\psi\left(k+1\right)+\psi\left(n+k+1\right)}{k!(n+k)!}\sin\left(\tfrac{3%
}{4}n\pi+\tfrac{1}{2}k\pi\right)(\tfrac{1}{4}x^{2})^{k}.\]