I fully agree with this analysis. There is for sure a bug because all the "mixed terms" (those containing a[1]*a[2]) are missing and all the "pure terms" (those containing a[1]*a[1] and a[2]*a[2]) give a result that is the double of the correct one. The semantic problem is that each Sum should have a distinct index. Is there a workaround to this bug ? Take into account that I have many such series to manipulate so my goal was not just to report a bug, but especially to devise a workaround. Thanks, Enrico

I fully agree with this analysis. There is for sure a bug because all the "mixed terms" (those containing a[1]*a[2]) are missing and all the "pure terms" (those containing a[1]*a[1] and a[2]*a[2]) give a result that is the double of the correct one. The semantic problem is that each Sum should have a distinct index. Is there a workaround to this bug ? Take into account that I have many such series to manipulate so my goal was not just to report a bug, but especially to devise a workaround. Thanks, Enrico

The expression for fsquared2(x) was just reported because it's the best result that I have achieved in trying to transform the square of a Sum in a double Sum, that is my final goal. To this purpose I have tried many commands, including simplify and combine (with trig) and accidentally I noticed that taking the derivative of the indefinite integral somehow induced a behavior that seemed to be closer to my goal (appearance of Sum(Sum(....) I think that the trigonometric identity cited by you is correct but the fsquared2(x) resulting from its substitution is not correct as well. I hope to have been clearer concerning what is my real question. Thanks. Enrico

The expression for fsquared2(x) was just reported because it's the best result that I have achieved in trying to transform the square of a Sum in a double Sum, that is my final goal. To this purpose I have tried many commands, including simplify and combine (with trig) and accidentally I noticed that taking the derivative of the indefinite integral somehow induced a behavior that seemed to be closer to my goal (appearance of Sum(Sum(....) I think that the trigonometric identity cited by you is correct but the fsquared2(x) resulting from its substitution is not correct as well. I hope to have been clearer concerning what is my real question. Thanks. Enrico