Similarity With An Integration By Parts
The formula for an integration by parts is
Beside the boundary conditions, we notice that the first integral contains two multiplied functions, one which is integrated in the final integral ( becomes ) and one which is differentiated ( becomes ).
The process of the Abel transformation is similar, since one of the two initial sequences is summed ( becomes ) and the other one is differenced ( becomes ).
Read more about this topic: Summation By Parts
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