Gudermannian function

Summary

Gudermannian function is a mathematical concept^[1]. It draws 86 Wikipedia views per month (mathematical_concept category, ranking #180 of 1,007).^[2]

Key Facts

• Gudermannian function's image is recorded as Gudermannian graph.png^[3].
• Gudermannian function's instance of is recorded as mathematical concept^[4].
• Christoph Gudermann is named after Gudermannian function^[5].
• Gudermannian function's subclass of is recorded as function^[6].
• Gudermannian function's Commons category is recorded as Gudermannian function^[7].
• Gudermannian function's Freebase ID is recorded as /m/01s50p^[8].
• Gudermannian function's defining formula is recorded as \operatorname{gd} \psi \equiv \int_0^\psi \operatorname{sech} t \mathrm{~d} t \quad \forall \psi \in (-\infty, \infty)^[9].
• Gudermannian function's MathWorld ID is recorded as GudermannianFunction^[10].
• Gudermannian function's MathWorld ID is recorded as Gudermannian^[11].
• Gudermannian function's schematic is recorded as Gudermannian function.png^[12].
• Gudermannian function's maintained by WikiProject is recorded as WikiProject Mathematics^[13].
• Gudermannian function's Microsoft Academic ID is recorded as 22334761^[14].
• Gudermannian function's in defining formula is recorded as \operatorname{gd}^[15].
• Gudermannian function's in defining formula is recorded as \operatorname{sech}^[16].
• Gudermannian function's Namuwiki ID is recorded as 구데르만 함수^[17].
• Gudermannian function's power series expansion is recorded as \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^[18].

Why It Matters

Gudermannian function draws 86 Wikipedia views per month (mathematical_concept category, ranking #180 of 1,007).^[2] It has Wikipedia articles in 15 language editions, a strong signal of global cultural recognition.^[19] It is known by 12 alternative names across languages and contexts.^[20]