Abel–Plana formula

GPTKB entity

Statements (14)
Predicate Object
gptkbp:instanceOf gptkb:mathematical_concept
gptkbp:appliesTo holomorphic functions
gptkbp:field complex analysis
gptkbp:hasEquation \sum_{n=0}^\infty f(n) = \int_0^\infty f(x) dx + \frac{f(0)}{2} + i \int_0^\infty \frac{f(it) - f(-it)}{e^{2\pi t} - 1} dt
gptkbp:namedAfter gptkb:Giovanni_Antonio_Amedeo_Plana
gptkb:Niels_Henrik_Abel
gptkbp:publishedIn gptkb:19th_century
gptkbp:relatedTo integral representation
summation of series
gptkbp:usedFor analytic continuation
evaluation of sums
gptkbp:bfsParent gptkb:Niels_Henrik_Abel
gptkbp:bfsLayer 6
https://www.w3.org/2000/01/rdf-schema#label Abel–Plana formula