Gudermannian

The Gudermannian $\mathrm{gd}$ is defined for $x \in \mathbb{R}$ by the formula $$\mathrm{gd}(x) = \displaystyle\int_0^x \dfrac{1}{\cosh t} \mathrm{d}t$$

• 

  Graph of $\mathrm{gd}$.

• 

  Domain coloring of $\mathrm{gd}$.

Properties

Derivative of Gudermannian
Taylor series for Gudermannian
Relationship between sine, Gudermannian, and tanh
Relationship between cosine, Gudermannian, and sech
Relationship between tangent, Gudermannian, and sinh
Relationship between csc, Gudermannian, and coth
Relationship between secant, Gudermannian, and cosh
Relationship between cot, Gudermannian, and csch

<center>$\ast$-integral functions

Cosine integral

Cosh integral

Exp integral $E_n$

Exp integral $\mathrm{Ei}$

Fresnel $C$

Fresnel $S$

Gudermannian

Inverse $\mathrm{gd}$

Sine integral

Log integral

Sinh integral

</center>