Gudermannian function
function that relates the circular functions and hyperbolic functions without using complex numbers
Facts
7 properties- Instance of
- mathematical concept
- Defining formula
- \operatorname{gd} \psi \equiv \int_0^\psi \operatorname{sech} t \mathrm{~d} t \quad \forall \psi \in (-\infty, \infty)[4]
- Maintained by WikiProject
- WikiProject Mathematics[5]
- Named after
- Christoph Gudermann[2]
- Power series expansion
- \operatorname{gd} z = \sum_{k=0}^\infty \frac{E_k}{(k+1)!}z^{k+1}= z - \frac16z^3 + \frac1{24}z^5 - \frac{61}{5040}z^7 + \frac{277}{72576}z^9 - \dots[8]
🏷️ Also known as
en hyperbolic amplitude
en Gudermannian
en Gudermannian function
ar دالة غودرمانية
ar دالة جودرمان
ar دالة جودرمانية
ar دالة غودرمان
de Gudermannfunktion
es función de Gudermann
fi Gudermannian
fi Gudermannin funktio
fr fonction de Gudermann
fr Gudermannien
hu Gudermann-függvény
it funzione gudermanniana
ja グーデルマン関数
ko 구데르만 함수
nl Gudermann functie
nl Gudermannfunctie
pl Amplituda hiperboliczna
🔖 Identifiers · 5
- Image (Wikimedia Commons)
- Gudermannian graph.png ↗
- Freebase ID
- /m/01s50p
- MathWorld ID
- GudermannianFunction, Gudermannian
- Microsoft Academic ID (discontinued)
- 22334761
- Namuwiki ID
- 구데르만 함수
🔗 Connections
Created notable works 1
Maintained by WikiProject 1
Named after 1
Subclass of 1
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Summary
Gudermannian function is a mathematical concept[1].