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Gauss’ Second Theorem for F 1 2 ( 1 / 2 ) -Series and Novel Harmonic Series Identities

Author

Listed:
  • Chunli Li

    (School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China)

  • Wenchang Chu

    (Department of Mathematics and Physics, University of Salento, 73100 Lecce, Italy)

Abstract

Two summation theorems concerning the F 1 2 ( 1 / 2 ) -series due to Gauss and Bailey will be examined by employing the “coefficient extraction method”. Forty infinite series concerning harmonic numbers and binomial/multinomial coefficients will be evaluated in closed form, including eight conjectured ones made by Z.-W. Sun. The presented comprehensive coverage for the harmonic series of convergence rate “ 1 / 2 ” may serve as a reference source for readers.

Suggested Citation

  • Chunli Li & Wenchang Chu, 2024. "Gauss’ Second Theorem for F 1 2 ( 1 / 2 ) -Series and Novel Harmonic Series Identities," Mathematics, MDPI, vol. 12(9), pages 1-12, May.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:9:p:1381-:d:1387344
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