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The inverse incomplete gamma function invigamma(a,p) returns the value z such that p = igamma(a,z). p is limited to (0;1]. a must be a positive real number. The implementation in gnuplot has relative accuracy that ranges from 1.e-16 for a<1 to 5.e-6 for a = 1.e10. Convergence may fail for a < 0.005.