Abel-Plana formula

proper noun

A summation formula stating that ∑ₙ₌₀ ᪲f(a+n)=∫ₐ ᪲f(x)dx+(f(a))/2+∫₀ ᪲(f(a-ix)-f(a+ix))/(i(e^(2πx)-1))dx.

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Meanings

proper nounthe Abel-Plana formula
  1. mathematicsA summation formula stating that ∑ₙ₌₀ ᪲f(a+n)=∫ₐ ᪲f(x)dx+(f(a))/2+∫₀ ᪲(f(a-ix)-f(a+ix))/(i(e^(2πx)-1))dx.

Origin

Discovered independently by Niels Henrik Abel (1823) and Giovanni Antonio Amedeo Plana (1820).

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Cite this entry
APA

Abel-Plana formula. (n.d.). In WatkinsX Dictionary. Retrieved November 5, 2026, from https://dictionary.watkinsx.com/word/Abel-Plana%20formula

MLA

“Abel-Plana formula.” WatkinsX Dictionary, https://dictionary.watkinsx.com/word/Abel-Plana%20formula. Accessed November 5, 2026.

Chicago

WatkinsX Dictionary, s.v. “Abel-Plana formula,” accessed November 5, 2026, https://dictionary.watkinsx.com/word/Abel-Plana%20formula.

Source: Abel-Plana formula on Wiktionary, CC BY-SA 4.0.