sh

The hyperbolic sine is defined as sinh z congruent 1/2(e^z - e^(-z)). The notation sh z is sometimes also used (Gradshteyn and Ryzhik 2000, p. xxix). It is implemented in the Wolfram Language as Sinh[z]. Special values include sinh0 | = | 0 sinh(ln ϕ) | = | 1/2, where ϕ is the golden ratio.

beta exponential function | bipolar coordinates | bipolar cylindrical coordinates | bispherical coordinates | catenary | catenoid | conical function | cubic equation | de Moivre's identity | Dixon-Ferrar formula | elliptic cylindrical coordinates | Elsasser function | Gudermannian | helicoid | Helmholtz differential equation--elliptic cylindrical coordinates | hyperbolic cosecant | hyperbolic functions | inverse hyperbolic sine | Laplace's equation--bispherical coordinates | Laplace's equation--toroidal coordinates | Lebesgue constants | Lorentz group | Mercator projection | Miller cylindrical projection | modified Bessel function of the second kind | modified spherical Bessel function of the first kind | modified Struve function | Nicholson's formula | oblate spheroidal coordinates | parabola involute | partition function P | Poinsot's spirals | prolate spheroidal coordinates | Schläfli's formula | Shi | sine | sine-Gordon equation | surface of revolution | tau function | toroidal coordinates | toroidal function | tractrix | Watson's formula