The Gudermannian function, or hyperbolic amplitude, is named after him.
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*The Gudermannian also appears in a moving mirror solution of the dynamical Casimir effect.
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:It looks like the Gudermannian function article might be of some use to you.
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The Gudermannian function gives a direct relationship between the circular functions and the hyperbolic ones that does not involve complex numbers.
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I don't think the species has been named; perhaps call them " inverse-Gudermannian identities " ?-- Talk 15 : 57, 23 September 2006 ( UTC)
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Besides the logistic function, sigmoid functions include the ordinary hyperbolic tangent, the Gudermannian function, and the error function, but also the generalised logistic function and algebraic functions like f ( x ) = \ tfrac { x } { \ sqrt { 1 + x ^ 2 } }.
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