Borwein et al. (2004, pp. 4 and 44) term the expression of the integrals
(OEIS A083648 and A073009)
in terms of infinite sums "a sophomore's dream."
For ,
write
Integrating term by term then gives
(Borwein et al. 2004, p. 44).
For ,
write
Integrating term by term then gives
(Borwein et al. 2004, pp. 4 and 44).
See also
Power Tower
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References
Borwein, J.; Bailey, D.; and Girgensohn, R. Experimentation in Mathematics: Computational Paths to Discovery. Wellesley, MA: A K Peters,
2004.Dunham, W. The
Calculus Gallery: Masterpieces from Newton to Lebesgue. Princeton, NJ: Princeton
University Press, pp. 46-51, 2005.Sloane, N. J. A. Sequences
A083648 and A073009
in "The On-Line Encyclopedia of Integer Sequences."Referenced
on Wolfram|Alpha
Sophomore's Dream
Cite this as:
Weisstein, Eric W. "Sophomore's Dream."
From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SophomoresDream.html
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