I have found an approximation for the iterated product:

when x is non-integer value.

this product is important because it is resulted in the first derive of

Now! after some logical sequences I made an approximation as below:

Let x = u + v , while u is integer and 0 < v < 1

then the approximation for is

I can varify it is exactly correct for min v and max v values.

but I can't make sure for v , if v for example equal 0.5 because I don't have Measuring tools or software to compare the variances

I need help.

when x is non-integer value.

this product is important because it is resulted in the first derive of

Now! after some logical sequences I made an approximation as below:

Let x = u + v , while u is integer and 0 < v < 1

then the approximation for is

I can varify it is exactly correct for min v and max v values.

but I can't make sure for v , if v for example equal 0.5 because I don't have Measuring tools or software to compare the variances

I need help.