Havil's book "Gamma" page 57, formula

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The discussion centers on a formula from Havil's book "Gamma," specifically on page 57, where a participant questions the origin of the numeral 1 in the last line of the formula. It is concluded that the last sum should indeed start at 1, which is crucial for the application of integration by parts. The term for r=0 is identified as special and can be handled separately, suggesting a potential copy-paste error in the text.

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Lapidus
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Where does the 1 in the last line come from?

Thank you!
 
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Looks like the last sum should start at ##1##, which I guess would be important when integration by parts is used. The term for ##r=0## is somehow special and can be treated separately. Probably a copy+paste error.
 
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