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# Sech

 Sech[z]gives the hyperbolic secant of z.
• Mathematical function, suitable for both symbolic and numerical manipulation.
• .
• For certain special arguments, Sech automatically evaluates to exact values.
• Sech can be evaluated to arbitrary numerical precision.
• Sech automatically threads over lists.
Evaluate numerically:
 Scope   (11)
Evaluate to high precision:
The precision of the output tracks the precision of the input:
Sech threads element-wise over lists and matrices:
Evaluate for complex arguments:
Simple exact purely imaginary values are generated automatically:
Convert multiple-angle expressions:
Find factors of decomposition:
Convert sums of hyperbolic functions to products:
Expand assuming real variables:
Convert to exponentials:
Sech can deal with real-valued intervals:
Infinite arguments give symbolic results:
Sech can be applied to power series:
 Applications   (5)
Plot a tractrix pursuit curve:
Plot a pseudosphere:
Calculate the finite area of the surface extending to infinity:
A soliton in the Korteweg-de Vries equation:
A Schrödinger equation with a zero energy solution:
Calculate the CDF of the hyperbolic secant PDF:
Plot the PDF and CDF:
Basic parity and periodicity properties of Sech get automatically applied:
Expressions containing hyperbolic functions do not automatically simplify:
Use Refine, Simplify, and FullSimplify to simplify expressions containing Sech:
Use FunctionExpand to express special values in radicals:
Compose with inverse functions:
Solve a hyperbolic equation:
Numerically find a root of a transcendental equation:
Reduce a hyperbolic equation:
Integrals:
Integral transforms:
Obtain Sech from sums, products, and integrals:
Sech appears in special cases of special functions:
Sech is a numeric function:
Machine-precision input is insufficient to give a correct answer:
With exact input, the answer is correct:
A larger setting for \$MaxExtraPrecision can be needed:
The inverse of Sech evaluates to Cosh:
No power series exists at infinity, where Sech has an essential singularity:
In traditional form parentheses are needed around the argument: