The following formula is involved in the calculation of probability density function (PDF) values for the chi-square distribution:
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Chi-square distribution probability density function (PDF):

where k is the degrees of freedom, and Γ is the gamma function.
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The following references can be used to cite this probability density function (pdf) calculator for the chi-square distribution:
 | Soper, D.S. (2013). Probability Density Function (PDF) Calculator for the Chi-Square Distribution [Software]. Available from http://www.danielsoper.com/statcalc |
 | Abramowitz, M. and Stegun, I.A., eds. (1965). Handbook of Mathematical Functions. New York, NY: Dover. |