## 10 Reputation

9 years, 330 days

## difficult integration from zero to infin...

Maple 11

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity);

restart; with(LinearAlgebra); int(exp(-(ln(z/(snr*B^2))+4*sigma^2)^2/(32*sigma^2))*eta^2*(y/z)^((1/2)*eta^2-1)/(z*sqrt(32*Pi*sigma^2)*(2*sqrt(y*z))*(2*A[o]^(eta^2))), z, z = y/A[o]^2 .. infinity)

## cross correlation of log-normal pdfs...

Please I want to know how to solve this integration.

int(exp(-(ln(y)-2*sigma^2)^2/(8*sigma^2))/(y*sqrt(8*Pi*sigma^2))*exp(-(ln(y+z)-2*sigma^2)^2/(8*sigma^2))/((y+z)*sqrt(8*Pi*sigma^2)), y = 0 .. infinity)

## Closed Form Expression of Double Integra...

Maple

restart;

with(LinearAlgebra);

rho := .25; sigma := .1; SNR := 25;

a := (32*12)*Pi*sqrt(1-rho^2...

## long memory integration...

Maple

`restart;with(LinearAlgebra); with(linalg);`
`Q := x->0.5*erfc(x/sqrt(2));`
`rho:=0.25;sigma := 0.3;`
`m1 := sigma*sigma*Matrix(3, 3, [1, rho, rho^2, rho, 1, rho, rho^2, rho, 1]);`
`SNR := 15; mu := evalf(10^(.1*SNR));`
` `
` a := Matrix(1, 3, [(ln(y/mu)+4*sigma^2)^2, (ln(y1/mu)+4*sigma^2)^2,`
` (ln(y2/mu)+4*sigma^2)^2]);`

## Difficult Integration...

Maple
`Please Help me:`
`First to solve this integration note that it is working if sigma=0.1.`
`Secondly I want to increase the accuracy of the result of sigma=0.1 as`
`there is slight difference between this numerical integration and montecarlo simulation `
`using MATLAB.`
` `
`restart;Q := x->0.5*erfc(x/sqrt(2));sigma := 0.3;SNR := [seq(1 .. 25, 1)]; for i in SNR do mu := evalf(10^(.1*i));`
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