Introductio in analysin infinitorum¶
Euler, L. (1748). Introductio in analysin infinitorum.
Cited by¶
4 citations across 4 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
Domain-specific¶
Verification¶
This reference passed the adversarial substantiation pipeline: it was checked to exist and to support the claim it is attached to. See how references were verified.
Links previously used in the corpus¶
Before the registry existed this work was also linked 1 other way.
Registry ID ref:88b57a0c1baa · see in the full table