is there a way to explicitly express the chi-squared inverse function? when programming it, I have had to resort to a guessing system where I find a chi value that is too low and too high, and evaluate the chi-squared CDF to reset the high and low points iteratively until it is within a preset tolerance to the correct value. However, this a clunky and inefficient method. Additionally, for large degrees of freedom (50,000 or so) I can't even calculate the chi-squared CDF because the values are too high. I noticed that this function can be expressed as a ratio of the gamma function and incomplete gamma function, so It occured to me to express the value as a difference of logs of each piece. However, I have only found expressions of the incomplete gamma function as sums, which are difficult (impossible?) to log. is there any way to express the incomplete gamma function as a product?