The Gudermannian function reference article from the English Wikipedia on 24-Apr-2004 (provided by Fixed Reference: snapshots of Wikipedia from wikipedia.org)

Gudermannian function

The Gudermannian function relates the circular and hyperbolic trigonometric functions without resorting to complex numbers. It is defined by

The following identities follow:

The inverse,

is the core of the Mercator projection.

The following identities also hold:

Ref: CRC Handbook of Mathematical Sciences 5th ed. pp323–5

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