Hi,

I am sorry about the uploaded file format. I have just included the same piece of code in simple text. I had used the 2D input just to show the behaviour of the function with different input values as the deviation of the result from the expected value is not quite visble for 1D input. 

Digits := 50: interface(displayprecision = 3):

a := 1: C := 1.000: L := 4: CS := C*L:  result := array(1 .. 10):  ind := 1:

for rangedb from -5 by 5 to 40 do

y := 10^((1/10)*rangedb):

R := C/y:

r := R/(a+L*R):

result[ind] := simplify((Product(GAMMA(1+CS)*GAMMA(1+CS+(L-n+1)*r)*hypergeom([1+CS, 1], [1+C], r)/(GAMMA(r+1+CS)*GAMMA(1+CS+(L-n)*r)), n = 1 .. L-1))*hypergeom([1+CS, 1], [1+C], r)):

ind := ind+1:

end do:

print(result)

[17.695        11.074      4.878      2.141      1.333     1.102     1.032      1.010    1.003    1.001]

Expected result by directly computing the series form of Lauricella function is

[108.4473    26.0417   6.2848   2.2387    1.3409  1.1025   1.0319    1.0100   1.0032   1.0010].

Axel, Your previous post was very informative, thanks, but the formula for the original case given by you seeems to be bit different from what I was trying to evaluate in the sense that expression term given by you

GAMMA(1+(C+r)*L)/GAMMA((C+r)*L+1-3*r) is actually

GAMMA(1+(C+r)*L)/GAMMA(1+(C+r)*L-r). Though I could not make out how it was obtained in your case, but the numerical values seems to be bit different.

Regarding the convergence issue, I was commenting on the behaviour of the Lauricella function output from the above method for a range of inputs, i.e. deviation at the values |x1|+|x2|+..+|xL| closer to unity. I am not sure is there some cancellation error as pointed out by you earlier but its not getting healed by increasing the precision. I have just uploaded the article for your reference [Equations 3,5,9 and 10].

Thanks a lot,

Vish

Download 8014_Some decomposition formulas.pdf
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Hi alec,

 Thanks for the reply. I have attached the maple worksheet with the details and the reason for the values to be expected to be closer. Please have a look. I was wondering is there anyway to get rid of the huge variable resolution issue. Thanx for the help.

Best regards,

Vishwa

View 8014_Hypergeometric-diff.mw on MapleNet or Download 8014_Hypergeometric-diff.mw
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