Change of Variables

Q: How can I compute the following integral?

[Graphics:inoutbgr2.gif][Graphics:inoutbgr40.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr41.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr42.gif]

B. Schnizer (schnizer@itp.tu-graz.ac.at) answers: Use the following (translational) substitution to simplify the exponential function:

[Graphics:inoutbgr2.gif][Graphics:inoutbgr43.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr44.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr45.gif]

The integration limits are unaffected and we obtain

[Graphics:inoutbgr2.gif][Graphics:inoutbgr46.gif]
[Graphics:inoutbgr2.gif][Graphics:inoutbgr47.gif]

which agrees with [Gradshteyn and Ryzhik 1980, 3.896.4].