Hyperbolic Cosecant Function for Numeric and Symbolic Arguments

Depending on its arguments,cschreturns floating-point or exact symbolic results.

Compute the hyperbolic cosecant function for these numbers. Because these numbers are not symbolic objects,cschreturns floating-point results.

A = csch([-2, -pi*i/2, 0, pi*i/3, 5*pi*i/7, pi*i/2])

A = -0.2757 + 0.0000i 0.0000 + 1.0000i Inf + 0.0000i... 0.0000 - 1.1547i 0.0000 - 1.2790i 0.0000 - 1.0000i

Compute the hyperbolic cosecant function for the numbers converted to symbolic objects. For many symbolic (exact) numbers,cschreturns unresolved symbolic calls.

symA = csch(sym([-2, -pi*i/2, 0, pi*i/3, 5*pi*i/7, pi*i/2]))

symA = [ -1/sinh(2), 1i, Inf, -(3^(1/2)*2i)/3, 1/sinh((pi*2i)/7), -1i]

Usevpato approximate symbolic results with floating-point numbers:

vpa(symA)

ans = [ -0.27572056477178320775835148216303,... 1.0i,... Inf,... -1.1547005383792515290182975610039i,... -1.2790480076899326057478506072714i,... -1.0i]

Plot Hyperbolic Cosecant Function

Plot the hyperbolic cosecant function on the interval from -10 to 10.

symsxfplot(csch(x),[-10 10]) gridon

Handle Expressions Containing Hyperbolic Cosecant Function

Many functions, such asdiff,int,taylor, andrewrite, can handle expressions containingcsch.

Find the first and second derivatives of the hyperbolic cosecant function:

syms x diff(csch(x), x) diff(csch(x), x, x)

ans = -cosh(x)/sinh(x)^2 ans = (2*cosh(x)^2)/sinh(x)^3 - 1/sinh(x)

Find the indefinite integral of the hyperbolic cosecant function:

int(csch(x), x)

ans = log(tanh(x/2))

Find the Taylor series expansion ofcsch(x)aroundx = pi*i/2:

taylor(csch(x), x, pi*i/2)

ans = ((x - (pi*1i)/2)^2*1i)/2 - ((x - (pi*1i)/2)^4*5i)/24 - 1i

Rewrite the hyperbolic cosecant function in terms of the exponential function:

rewrite(csch(x), 'exp')

ans = -1/(exp(-x)/2 - exp(x)/2)