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Full Version: CAS: Hyperoblic CAS Transformations
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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