2E(k)π
=
1−122k2−12⋅322⋅42k4−(1⋅3⋅524⋅3)2k65−(1⋅3⋅5⋅727⋅3)2k87−⋯−[(2n−1)!!2nn!]2k2n2n−1−⋯
Gradshteyn & Ryzhik (1965), §8.114.1