FoxTrot Series
The "Foxtrot series" is a mathematical sum that appeared in the June 2, 1996 comic strip FoxTrot by Bill Amend (Amend 1998, p. 19; Mitchell 2006/2007). It arose from a convergence testing problem in a calculus book by Anton, but was inadvertently converted into a summation problem on an alleged final exam by the strip's author:
The sum can be done using partial fraction decomposition to obtain
![👁 1/3(1-ln2)+(zeta^2)/3sum_(n=1)^(infty)(-1)^n(1-2n)×[1/((1+zeta)(zeta-n))+1/((1+zeta)(zeta^2+n))]](https://mathworld.wolfram.com/images/equations/FoxTrotSeries/Inline6.svg){kind=link}
![👁 1/3[1-ln2+pisech(1/2sqrt(3)pi)]](https://mathworld.wolfram.com/images/equations/FoxTrotSeries/Inline9.svg){kind=link}
(OEIS A127198), where 👁 zeta=(-1)^(1/3)=(1+isqrt(3))/2
and the last sums have been done
in terms of the digamma function and symbolically
simplified.
See also
Digamma Function, SeriesExplore with Wolfram|Alpha
More things to try:
References
Amend, B. Camp FoxTrot. Kansas City, MO: Andrews McMeel, p. 19, 1998.Mitchell, C. W. Jr. In "Media Clips" (Ed. M. Cibes and J. Greenwood). Math. Teacher 100, 339, Dec. 2006/Jan. 2007. Sloane, N. J. A. Sequence A127198 in "The On-Line Encyclopedia of Integer Sequences."Referenced on Wolfram|Alpha
FoxTrot SeriesCite this as:
Weisstein, Eric W. "FoxTrot Series." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/FoxTrotSeries.html