numerical solution to a set of equations with hypergeometric function

• To: mathgroup at smc.vnet.net
• Subject: [mg126120] numerical solution to a set of equations with hypergeometric function
• From: Joseph Döner <doenermachtscheisse at googlemail.com>
• Date: Thu, 19 Apr 2012 03:54:04 -0400 (EDT)
• Delivered-to: l-mathgroup@mail-archive0.wolfram.com

```Hi,

i ran into some trouble solving the following set of equations
http://imageshack.us/photo/my-images/337/gleichungen.jpg/ for N and M,
all other variables are known. I think the problem lies within the F-
function. It's supposed to be the hypergeometric function.
I used FindRoot and the hypergeometric2f1regularized command at first,
but all i got were some errors. When i tried to solve it with the
integral representation and the power series of the function I still
didn't get any results. If i insert all the values it does look like
this:

FindRoot[{((0.5*0.5 + 0.5*0.5)*(2.5*Hypergeometric2F1Regularized[1,
1.894427191, 2.894427191, -G/M] +
1.180339887*Hypergeometric2F1Regularized[1, 0.894427191,1.894427191, -
M/G]))/(1 - (0.5 - G)*(2.5*Hypergeometric2F1Regularized[1,
1.894427191, 2.894427191, -G/M] +
1.180339887*Hypergeometric2F1Regularized[1, 0.894427191,  1.894427191,
-M/G]) - (0.5 - M)*(1.180339887*Hypergeometric2F1Regularized[1,
1.894427191, 2.894427191, -M/G] -
(-2.5)*Hypergeometric2F1Regularized[1, 0.894427191, 1.894427191, -G/
M])) == (((1 - 0.5)*0.5 + (1 -
0.5)*0.5)*(50*Hypergeometric2F1Regularized[1, 1.2, 2.2, -(1 - G)/(1 -
M)] + 8.3333333*Hypergeometric2F1Regularized[1, 0.2, 1.2, -(1 - M)/(1
- G)]))/(1 - (G - 0.5)*(50*Hypergeometric2F1Regularized[1, 1.2, 2.2, -
(1 - G)/(1 - M)] + 8.3333333*Hypergeometric2F1Regularized[1, 0.2, 1.2,
-(1 - M)/(1 - G)]) - (M -
0.5)*(8.333333*Hypergeometric2F1Regularized[1, 1.2, 2.2, -(1 - M)/(1 -
G)] - (-50)*Hypergeometric2F1Regularized[1, 0.2, 1.2, -(1 - G)/(1 -
M)])), ((0.5*0.5 +
0.5*0.5)*(1.180339887*Hypergeometric2F1Regularized[1, 1.894427191,
2.894427191, -G/M] + 8.33333*Hypergeometric2F1Regularized[1, 0.2, 1.2,
-M/G]))/(1 - (0.5 -
G)*(1.180339887*0.5/0.5*Hypergeometric2F1Regularized[1, 1.1894427191,
2.894427191, -M/G] - (-2.5)*Hypergeometric2F1Regularized[1,
0.894427191, 1.894427191, -G/M])) == (((1 - 0.5)*0.5 + (1 -
0.5)*0.5)*(8.3333333*Hypergeometric2F1Regularized[1, 0.2, 1.2, (1 - M)/
(1 - G)]))/(1 - (G -  0.5)*(50*Hypergeometric2F1Regularized[1, 1.2,
2.2, -(1 - G)/(1 - M)] + 8.3333333*Hypergeometric2F1[1, 0.2, 1.2, -(1
- M)/(1 - G)]) - (M - 0.5)*(8.333333*Hypergeometric2F1Regularized[1,
1.2, 2.2, -(1 - M)/(1 - G)] - (-50)*Hypergeometric2F1Regularized[1,
0.2, 1.2, -(1 - G)/(1 - M)]))}, {{G, 0.5}, {M, 0.5}}]

If you have any idea why it does not work, let me now :)