Introductio in Analysin Infinitorum¶
Euler, L. (1748). Introductio in Analysin Infinitorum.
Cited by¶
3 citations across 3 artifacts.
Each citation links to the sentence it supports in the citing article.
Primes¶
- Exponentiation
- … arithmetic, exponential functions (`e^x`, `2^x`, `10^x`) in calculus and analysis, logarithms as the inverse operation (Napier 1614 introducing the original logarithm tables and Burgi independently around the same period; Euler's eighteenth-century formalization establishing `e ≈ 2.71828` as the natural base
This sourceconfirmed — systematic analytical-function treatment of e^x; computes e to 18 places, gives the exponential series, and underpins Euler's identity (e^{iπ} = −1); established much of the modern exponential/logarithmic framework.
- … arithmetic, exponential functions (`e^x`, `2^x`, `10^x`) in calculus and analysis, logarithms as the inverse operation (Napier 1614 introducing the original logarithm tables and Burgi independently around the same period; Euler's eighteenth-century formalization establishing `e ≈ 2.71828` as the natural base
- Periodicity
- The exponential function `e^x` is not periodic on the real line, but the complex exponential `e^{iθ}` is periodic of period `2π` on the imaginary axis (`e^{i(θ + 2π)} = e^{iθ}` because `e^{2πi} = 1`); this complex-exponential periodicity, established in Euler's 1748 Introductio in analysin infinitorum
This source(Originating systematic treatment of the analytical-function viewpoint of `e^x`, the constant `e`, the identity `e^{iπ} = -1`, and the foundation of complex analysis. Two-volume work that established much of the modern notation and framework for exponential and logarithmic functions.)
- The exponential function `e^x` is not periodic on the real line, but the complex exponential `e^{iθ}` is periodic of period `2π` on the imaginary axis (`e^{i(θ + 2π)} = e^{iθ}` because `e^{2πi} = 1`); this complex-exponential periodicity, established in Euler's 1748 Introductio in analysin infinitorum
- Wave
- The mathematical formalism for linearized wave propagation was systematized by Euler in 1748
This source(Originating systematic treatment of the analytical-function viewpoint of `e^x`, the constant `e`, the identity `e^{iπ} = -1`, and the foundation of complex analysis. Two-volume work that established much of the modern notation and framework for exponential and logarithmic functions.)
- The mathematical formalism for linearized wave propagation was systematized by Euler in 1748
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