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2.5 Integral <AA||AB> over hyperbolic Prolate Spheroidal Coordinates



Place the integral in parentheses as I'. I and I' looks like follows.

① Integrate with electron 1. And we find I'.



Common for 2.4 <AB||AB>, 2.5 <AA||AB>, and 2.6 <AA||AA>
See 2.4 <AB||AB>.




② Integrate with electron 2. And we find I.












rA2 will be substituted later.


Set α=rAB/a0.


Here, we set I''1, I''2, and I''3 as follows.


We obtain I below.

And we will integrate I''1, I''2, and I''3 individually.

②-1 Integrate I''1.



MyLibrary 2-3-2




MyLibrary 1-1-2




②-2 Integrate I''2.

Here we use the next volume element.






MyLibrary 2-1-1

MyLibrary 2-1-3






MyLibrary 1-1-3

MyLibrary 1-1-1





②-3 Integrate I''3.




MyLibrary 2-1-1

MyLibrary 2-1-2






MyLibrary 1-1-2

MyLibrary 1-1-1





Getting I''1, I''2, and I''3 list as follows.


Introducing I''1, I''2, and I''3, we obtain I below.






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