Sum of alternating-like series as definite integrals

DOI10.1080/0020739X.2021.1949060zbMath1499.97006OpenAlexW3181457412WikidataQ114101601 ScholiaQ114101601MaRDI QIDQ5055056

Sergio A. Carrillo

Publication date: 12 December 2022

Published in: International Journal of Mathematical Education in Science and Technology (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/0020739x.2021.1949060

zbMATH Keywords

definite integralsAbel's continuity theoremGauss' digamma theorem

Mathematics Subject Classification ID

Convergence and divergence of series and sequences (40A05) Other functions defined by series and integrals (33E20) Sequences and series (educational aspects) (97I30) Integral calculus (educational aspects) (97I50)

Cites Work

• A theorem for the closed-form evaluation of the first generalized Stieltjes constant at rational arguments and some related summations
• On Gauss' formula for \(\psi\) and finite expressions for the \(L\)-series at 1
• A unified method for evaluating several infinite series
• A Short Elementary Proof of Σ 1/k²= π²/6
• Simple expansions for sine and cosine
• On the summation of subseries in closed form
• Euler constants for arithmetic progressions
• An Elementary Proof for Two Basic Alternating Series
• Finding sums for an infinite class of alternating series
• An infinite series involving inverse tan
• A Morsel from Euler
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