Problem in integration function containing gauss hypergeometric function

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Shweta Rajoria 2017-12-14

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评论： Shweta Rajoria 2018-1-9

I am deriving the coverage probability of heterogeneous network with massive MIMO macro base station. During the process, I am stuck in the in hypergeometric function. The small part of that program is given below.

fun= @(x,y)imag(exp(pi.*1i.*(x).*y.^(-2).*hypergeom(1,[1/2,3/2],-1i.*x./(y.^4))))./x
c=  @(y) integral(@(x) fun(x,y), 0.1,1,'ArrayValued',true)
fun1= @(y)((1/2)-((1/pi).*c(y))).*exp(-pi.*y.^2)
c1 = integral(fun1, 0.1,1)

I think iproblem is due to terms(y.^(-2) and and y.^4) in the fun. If any body have any idea please suggest. Any suggestions regarding this will be appreciated.

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Walter Roberson 2018-1-9

编辑：Walter Roberson 2018-1-9

To within the boundaries of double precision, c1 will be nan. The values involved are way way too big to work with in double precision.

Shweta Rajoria 2018-1-9

ok sir.. thank you.. but please guide me how this problem can be resolved.

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回答（1 个）

Walter Roberson 2018-1-8

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fun(8/10, 3/10) is about 2.974*10^1912918 .

fun(8/10, 2/10) is about 4.087*10^-24618734963806

fun(8/10, 0.18) is about 2.345*10^207906652598325658

So, fun is very steep, and has a lot of values that overflow floating point representation. You will not be able to integrate that using any normal representation.