# Using Product for different variables

when using product in mathematica the initial and maximum value of the product will be the variable itself that will be maupulated. what I need is to make these initial and maximum of the product as an index for several variables. for example if I have the following series product:

$$\text{y}=\prod _{i=1}^M \left(1-\exp \left(-\frac{z}{\bar{\gamma }_{\text{RD}_i}}\right) \left(\frac{\bar{\gamma }_{\text{SR}_i}}{z \bar{\gamma }_{\text{IR}_i}+\bar{\gamma }_{\text{SR}_i}}\right){}^L\right);$$

So here $i$ is the index for variables $\bar{\gamma }_{\text{RD}}$, $\bar{\gamma }_{\text{IR}}$, and $\bar{\gamma }_{\text{SR}}$

How I can perform this product? Note: L is Positive Integer; L=1,2,...

• And what have you tried so far? – Kuba Dec 2 '13 at 14:19
• @Kuba manually I can solve these kind of problems for simple equations. but when it comes with difficult and combined equations its not possible to solve by hand. – sky-light Dec 2 '13 at 14:23
• I meant, what have you done so far in Mathematica? – Kuba Dec 2 '13 at 14:25
• @Kuba according to the Mathematica documentations the initial and maximum value of the product will be the variable itself. I read these documentations. I didn't find the solution. that is why I asked here. reference.wolfram.com/mathematica/ref/Product.html – sky-light Dec 2 '13 at 14:39

You mean something like this?

m = 10;
gammaRD = ConstantArray[RandomReal[], {m}];
gammaIR = ConstantArray[RandomReal[], {m}];
gammaSR = ConstantArray[RandomReal[], {m}];
L1 = 3;
z = 5;
y = Product[
1 - Exp[-z/gammaRD[[i]]] gammaSR[[i]]/(gammaIR[[i]] + gammaSR[[i]]) L1, {i,1,m}];
N[%]

(*0.989724106426077*)