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Böhmer integral

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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

Consequently, Fresnel integrals can be expressed in terms of the Böhmer integrals as

The sine integral and cosine integral can also be expressed in terms of the Böhmer integrals

References

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  • Böhmer, Paul Eugen (1939). Differenzengleichungen und bestimmte Integrale (in German). Leipzig, K. F. Koehler Verlag.
  • Oldham, Keith B.; Myland, Jan; Spanier, Jerome (2010). An Atlas of Functions. Springer Science & Business Media. p. 401. ISBN 9780387488073.