Hello,
I need to use the confluent function of second kind, also known as
Tricomi function. It is implemented as kummerU() function in
fAsianOptions package, but I've found very inaccurate values, comparing
with those provided by Mathematica. I think Mathematica values are OK
because kummerU values leads to negative probabilities.
For example, if you try the kummerU() function example, you obtain:
x = c(0.001, 0.01, 0.1, 1, 10, 100, 1000)
a = 1/3; b = 2/3
U = Re ( kummerU(x, a = a, b = b) )
cbind(x, U)
x U Mathematica
[1,] 1e-03 1.827638e+00 1.82764
[2,] 1e-02 1.659957e+00 1.65996
[3,] 1e-01 1.341021e+00 1.34102
[4,] 1e+00 8.745968e-01 0.874597
[5,] 1e+01 4.548890e-01 0.454805
[6,] 1e+02 1.731286e+35 0.214970
[7,] 1e+03 -1.318568e+76 0.0999778
I've added a third column in the table with Mathematica values, where
you can see the great differences in the last values. I have a lot of
examples of these differences, with non very strange parameters values.
I've also tried to define the Tricomi function in relation to the usual
confluent function given by genhypergeo(), but errors are even greater.
Does anybody know another function or another way to define an accurate
version of Tricomi function?
--
Dr. Antonio José Sáez Castillo
Dpto. de Estadística e Investigación Operativa
Escuela Politécnica Superior de Linares
Universidad de Jaén
C/ Alfonso X El Sabio 28, 23700 Linares (Jaén) ESPAÑA
Tlf. y FAX +34 953 648578
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