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What does the min and max values of the index calculator tool calculates?

What you get using the max function is the maximum value between two arguments.

For example, when I write this formula max ( green ; rededge ) I get values from 0.17-0.27.

If I display only the green band I get values from 0.04 to 0.09

If I display only the red edge I get values from 0.17 to 0.27

So the max of these two bands (green and red edge) will be the values from the red edge.

For information: Generate a vegetation index