--Copyright The Numerical Algorithms Group Limited 1994.

--% Expression To Power Series
-- We compute series expansions of various functions using EXPR2UPS and STTF.
-- Author: Clifton J. Williamson
-- Date Created: 12 August 1992
-- Date Last Updated: 12 August 1992
-- Keywords: Taylor series
-- References:

-- Power series expansions around branch points
-- (Well not really, since we have x**2, not x.  Otherwise, our series
-- expansions would have fractional powers.)

f1 := taylor(1 - x**2,x = 0)

asin f1
sin %

acos f1
cos %

f2 := taylor(1 + x**2,x = 0)

acsc f2
csc %

asec f2
sec %

f3 := taylor(1 - (x - a)**2,x = a)

asin f3
sin %

acos f3
cos %

f4 := taylor(1 + (x - a)**2,x = a)

acsc f4
csc %

asec f4
sec %

f5 := taylor(%i + x**2,x = 0)

asinh f5
map(normalize,sinh %)

acosh f1
map(normalize,cosh %)

asech f2
sech %

acsch f1
map(normalize,csch %)

f6 := taylor(%i + (x - a)**2,x = a)

asinh f6
map(normalize,sinh %)

acosh f3
map(normalize,cosh %)

asech f4
sech %

acsch f3
map(normalize,csch %)
