In mathematics, a Böhmer integral is an integral introduced by Böhmer (1939) generalizing the Fresnel integrals.
α − 1
( x , α )
α − 1
Consequently, Fresnel integrals can be expressed in terms of the Böhmer integrals as
2 π
2 π
The sine integral and cosine integral can also be expressed in terms of the Böhmer integrals
π 2
π 2
{\displaystyle {\begin{aligned}\operatorname {Si} (x)&={\frac {\pi }{2}}-\operatorname {S} (x,0)\\[1ex]\operatorname {Ci} (x)&={\frac {\pi }{2}}-\operatorname {C} (x,0)\end{aligned}}}
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