Wave Propagation in Linear Media | re-examined

integration limit a or the rightmost extremum of f, whichever is greater, are
calculated. In the second case, the first n function values of f to the right of a
are sought. Note that in this case, f is supposed to return values only to the
right of the rightmost extremum. In any case, f must be of the form f[...][x]."
OscInt::usage =
"OscInt[f,fpartition,a,(opts)] returns the univariate integral of an oscillating
function f over the range (a,Infinity) by means of a partition extrapolation strategy.
The function f is required to of the form f[...][x], x being the
integration variable. Quadrature is carried out between successive partition points
defined by the function fpartition[...][x] that either returns the zeros of the
integrand or the argument of the oscillating part. The sequence of partition
points is computed by the function PartitionTable, the actual integration is carried
out with the function PartInt. The first partition point can be given explicitly
with OscInt[f,fpartition,{a,a0},(opts)]. The options are passed to PartitionTable and
PartInt."
OscIntControlled::usage =
"OscIntControlled[f,fpartition,a,(opts)] works like OscInt with the additional
feature that the accuracy of the result may be specified in advance."
FunctionType::usage =
"FunctionType is an option for PartitionTable (and OscInt) that specifies how
the function passed to PartitionTable is to be interpreted.
FunctionType -> ZeroList means that the function returns consecutive zeros of the
integrand. FunctionType -> SinArgument or CosArgument means that it is the argument
function of the respective cyclic function."
ZeroList::usage =
"ZeroList is a value to FunctionType."
SinArgument::usage = CosArgument::usage =
"Argument is a value to FunctionType."
AccuracyControl::usage =
"AccuracyControl specifies whether the accuracy of the result of OscInt should
be controlled. With AccuracyControl -> n, at most MaxIterations are performed
to achieve the number of n correct digits. With AccuracyControl -> False, no
checking is done. The control loop uses the built-in function Accuracy."
IterationLength::usage =
"IterationLength specifies the number of terms that are added to the sequence
of partial sums with each iteration."
ApproxLimGeneric::nounique =
"There are `1` real solutions `2`, here is the largest.";
ApproxLimGeneric::nosolution =
"There is no positive real valued solution.";
QuadZero::noquad = "Function is not a quadratic polynomial";
ApproxLimQuad::noapprox = "No approximation needed";
ApproxLimLinear::noosc = "Function not infinitely oscillating";
ZerosInBetween::outside = "Function has no zeros inside the interval";
OscInt::lowfirst =
"First partition point is smaller than lower limit, only
`1` points are greater. This may cause problems.";
OscInt::badparam =
"\"`1`\" is no valid parameter for AccuracyControl.";
OscInt::accfail =
"OscInt failed to achieve the desired accuracy after `1` iterations. Increase
MaxIterations or lower AccuracyControl.";
PartitionTable::badparam =
"\"`1`\" is no valid parameter for FunctionType.";
Begin["`Private`"]
Options[OscInt] = {WorkingPrecision->$MachinePrecision,
AccuracyGoal->Infinity,
PrecisionGoal->Automatic,
MinRecursion->0,
MaxRecursion->20,
NSumTerms->10,
NSumExtraTerms->12,
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