Euler's beta integral in Pietro Mengoli's works
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Publication:1031944
DOI10.1007/s00407-009-0042-5zbMath1180.01018OpenAlexW2424529225MaRDI QIDQ1031944
Amadeu Delshams, Maria Rosa Massa Esteve
Publication date: 23 October 2009
Published in: Archive for History of Exact Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s00407-009-0042-5
beta functionbinomial coefficientbeta integralcombinatorial triangleharmonic trianglequasi-proportionWallis product
Factorials, binomial coefficients, combinatorial functions (05A10) Gamma, beta and polygamma functions (33B15) History of mathematics in the 17th century (01A45) History of special functions (33-03)
Related Items (4)
The Role of Indivisibles in Mengoli’s Quadratures ⋮ Proof pearl: Bounding least common multiples with triangles ⋮ Mengoli's mathematical ideas in Leibniz's excerpts ⋮ Proof Pearl: Bounding Least Common Multiples with Triangles
Cites Work
- Une histoire chinoise du ``nombre \(\pi\). (A Chinese history of the ``number \(\pi\))
- Symbolic language in early modern mathematics: The algebra of Pierre Hérigone (1580-1643)
- Cavalieri's method of indivisibles
- The ritual origin of the circle and square
- The calculus as algebraic analysis: Some observations on mathematical analysis in the 18th century
- Some aspects of Euler's theory of series: Inexplicable functions and the Euler-Maclaurin summation formula
- Mengoli on ``Quasi proportions
- Zhao Youqin and his calculation of \(\pi\)
- Differentials and differential coefficients in the Eulerian foundations of the calculus.
- Functions, functional relations, and the laws of continuity in Euler
- Leonhard Euler: The first St. Petersburg years (1727--1741)
- Algebra and geometry in Pietro Mengoli (1625--1686)
- The discovery of wonders: reading between the lines of John Wallis's \textit{Arithmetica infinitorum}
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