CAS: Hyperoblic CAS Transformations
11-27-2019, 01:58 PM
Post: #1
 Eddie W. Shore Senior Member Posts: 1,384 Joined: Dec 2013
CAS: Hyperoblic CAS Transformations
sinhexp

sinhexp(ϕ) = (e^(ϕ) - e^(-ϕ)) / 2 = ((e^ϕ)^2 - 1) / (2 * e^ϕ)
Code:
 #cas sinhexp(f):= BEGIN RETURN (e^(f)-e^(−f))/2 END; #end

coshexp

coshexp(ϕ) = (e^(ϕ) + e^(-ϕ)) / 2 = ((e^ϕ)^2 + 1) / (2 * e^ϕ)
Code:
 #cas coshexp(f):= BEGIN RETURN (e^(f)+e^(−f))/2 END; #end

tanhexp

tanhexp(ϕ) = (e^(ϕ) - e^(-ϕ)) / (e^(ϕ) + e^(-ϕ))
Code:
 #cas tanhexp(f):= BEGIN RETURN (e^(f)-e^(−f))/ (e^(f)+e^(−f)) END; #end

addsinh(ϕ + Ω) = sinh ϕ * cosh Ω + sinh Ω * cosh ϕ
Code:
 #cas addcosh(f,g):= BEGIN RETURN COSH(f)*COSH(g)+ SINH(f)*SINH(g); END; #end

addcosh(ϕ + Ω) = csoh ϕ * cosh Ω + sinh Ω * sinh ϕ
Code:
 #cas addsinh(f,g):= BEGIN RETURN SINH(f)*COSH(g)+ COSH(f)*SINH(g); END; #end

addtanh(ϕ + Ω) = (tanh ϕ + tanh Ω) / (1 + tanh ϕ * tanh Ω)
Code:
 #cas addtanh(f,g):= BEGIN RETURN (TANH(f)+TANH(g))/ (1+TANH(f)*TANH(g)); END; #end

Squaring Properties

sqsinh

sqsinh(ϕ) = sinh^2 ϕ = 1/2 * cosh(2 * ϕ) - 1/2
Code:
 #cas sqsinh(f):= BEGIN RETURN COSH(2*f)/2-1/2; END; #end

sqcosh

sqcosh(ϕ) = cosh^2 ϕ = 1/2 * cosh(2 * ϕ) + 1/2
Code:
 #cas sqcosh(f):= BEGIN RETURN COSH(2*f)/2+1/2; END; #end

Product Properties

sinhsinh

sinhsinh(ϕ, Ω) = 1/2 * (cosh(ϕ + Ω) - cosh(ϕ - Ω))
Code:
 #cas sinhsinh(f,g):= BEGIN RETURN 1/2*(COSH(f+g)- COSH(f-g)); END; #end

coshcosh

coshcosh(ϕ, Ω) = 1/2 * (cosh(ϕ + Ω) + cosh(ϕ - Ω))
Code:
 #cas coshcosh(f,g):= BEGIN RETURN 1/2*(COSH(f+g)+ COSH(f-g)); END; #end

sinhcosh

sinhcosh(ϕ, Ω) = 1/2 * (sinh(ϕ + Ω) + sinh(ϕ - Ω))
Code:
 #cas sinhcosh(f,g):= BEGIN RETURN 1/2*(SINH(f+g)+ SINH(f-g)); END; #end

Source:

Spiegel, Murray R. and Seymour Lipschutz, John Liu. Schuam's Outlines: Mathematical Handbook of Formulas and Tables 5th Edition McGraw Hill: New York 2018 ISBN 978-1-260-01053-4 compsystems Senior Member Posts: 1,337 Joined: Dec 2013