Titlebook: Calculus off the Beaten Path; A Journey Through It Ignacio Zalduendo Textbook 2022 The Editor(s) (if applicable) and The Author(s), under e

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The Gamma Function, it is easy to see that . Γ(0) is not defined, but we may use the equality . to define Γ in the interval (−1, 0), and then in (−2, −1), (−3, −2)…Thus, we consider Γ defined on all real numbers except {0, −1, −2, −3, …}. One value of Γ which is easy to calculate is . (see the Exercises).

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More Derivatives,xample, it may happen that . exists but may not be differentiable, in which case .″ does not exist. In this chapter we will suppose that our functions are infinitely differentiable, in other words, ., .″, ….., …, exist. But now what we want to ask ourselves is: what meaning does .″ have for our func

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More Integrals,n and without the area which they wanted to calculate. In the XVIIth Century Bonavantura Cavalieri (1598–1647) had an idea that was strongly criticized at the time: he considered an area as a “sum of lines” and a volume as a “sum of areas.”

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https://doi.org/10.1007/978-3-031-15765-3one-variable calculus; real functions; limits; derivatives; integrals; Riemann‘s rearrangement theorem; Py

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Calculus off the Beaten Path978-3-031-15765-3Series ISSN 1615-2085 Series E-ISSN 2197-4144