Böhmer integral

In mathematics, a Böhmer integral is an integral introduced by Böhmer (1939) generalizing the Fresnel integrals.

There are two versions, given by

$\displaystyle C(x,\alpha) = \int_x^\infty t^{\alpha-1}\cos(t) \, dt$

$\displaystyle S(x,\alpha) = \int_x^\infty t^{\alpha-1}\sin(t) \, dt$

References

• Böhmer, Paul Eugen (1939), Differenzengleichungen und bestimmte Integrale. (in German), Leipzig, K. F. Koehler Verlag