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HELP FOR: grlimit
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CALLING SEQUENCE: readlib ( grtools ):
grlimit ( expr, var, limit, fnList, valueList, LHlimit ):
PARAMETERS: expr - an expression
var - limiting variable
limit - limiting value of var
fnList - unspecified functions in expr
valueList - values of functions and/or their derivitives
w.r.t var at the limit point
LHlimit - (optional) limit to number of times L'Hopital's
rule should be applied (default = 8)
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SYNOPSIS:
- Evaluates expr at the limit point. If indeterminate forms arise then
L'Hopital's rule is applied (repeatedly) until the limit is resolved
or LH_limit is exceeded. If LH_limit is exceeded the indeterminate
portion is returned unevaluated.
- grlimit() works by substitution. It does not determine how rapidly
functions approach the limit point.
- Elements of valueList must consist of equations. The left-hand side of the
equations must be a STRING containing the function at the limit point.
Derivitives with respect to the limiting variable by a forward quote (').
See the example below for details.
- grlimit() first expands the expression and then evaluates term by term.
divergent terms are then lumped together, factored into a single
expression and that is then evaluated. This way divergent terms can
cancel in some cases. If the final result diverges grlimit() returns
infinity (regardless of whether it's -infinity or not).
- grlimit() is part of the grtools library. Load the library via
readlib ( grtools ):
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EXAMPLES:
> qload ( static ):
Default spacetime = static
For the static spacetime:
Coordinates
a
x = [ r, theta, phi, t ]
Line element
2
2 d r 2 2 2 2 2 2
ds = ------ + r d theta + r sin(theta) d phi - h(r) d t
h(r)
> grcalc ( Ricciscalar ):
> Rsc := grcomponent ( Ricciscalar );
> readlib ( grtools ):
> grlimit ( Rsc, r, 0, [h(r)], [`h(0)`=1,`h(0)'`=0] );
-6 h(0)''
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