11-27-2019, 01:58 PM
sinhexp
sinhexp(ϕ) = (e^(ϕ) - e^(-ϕ)) / 2 = ((e^ϕ)^2 - 1) / (2 * e^ϕ)
coshexp
coshexp(ϕ) = (e^(ϕ) + e^(-ϕ)) / 2 = ((e^ϕ)^2 + 1) / (2 * e^ϕ)
tanhexp
tanhexp(ϕ) = (e^(ϕ) - e^(-ϕ)) / (e^(ϕ) + e^(-ϕ))
Adding Properties
addsinh
addsinh(ϕ + Ω) = sinh ϕ * cosh Ω + sinh Ω * cosh ϕ
addcosh
addcosh(ϕ + Ω) = csoh ϕ * cosh Ω + sinh Ω * sinh ϕ
addtanh
addtanh(ϕ + Ω) = (tanh ϕ + tanh Ω) / (1 + tanh ϕ * tanh Ω)
Squaring Properties
sqsinh
sqsinh(ϕ) = sinh^2 ϕ = 1/2 * cosh(2 * ϕ) - 1/2
sqcosh
sqcosh(ϕ) = cosh^2 ϕ = 1/2 * cosh(2 * ϕ) + 1/2
Product Properties
sinhsinh
sinhsinh(ϕ, Ω) = 1/2 * (cosh(ϕ + Ω) - cosh(ϕ - Ω))
coshcosh
coshcosh(ϕ, Ω) = 1/2 * (cosh(ϕ + Ω) + cosh(ϕ - Ω))
sinhcosh
sinhcosh(ϕ, Ω) = 1/2 * (sinh(ϕ + Ω) + sinh(ϕ - Ω))
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
Blog Link: http://edspi31415.blogspot.com/2019/11/h...tions.html
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
Adding Properties
addsinh
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
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
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
Blog Link: http://edspi31415.blogspot.com/2019/11/h...tions.html