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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

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