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variants of this functions
InverseGammaRegularized






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > InverseGammaRegularized[a,z] > Differentiation > Low-order differentiation > With respect to z





http://functions.wolfram.com/06.12.20.0008.01









  


  










Input Form





D[InverseGammaRegularized[a, z], {z, 6}] == E^(6 w) w^(1 - 6 a) (1 - 120 a^5 + a^4 (274 + 600 w) - 3 a^3 (75 + 474 w + 400 w^2) + a^2 (85 + 3 w (399 + 874 w + 400 w^2)) + w (57 + 2 w (212 + w (437 + 60 w (5 + w)))) - a (15 + 2 w (216 + w (923 + w (1037 + 300 w))))) Gamma[a]^6 /; w == InverseGammaRegularized[a, z]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "6"]], "}"]]]]], RowBox[List["InverseGammaRegularized", "[", RowBox[List["a_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["6", " ", "w"]]], " ", SuperscriptBox["w", RowBox[List["1", "-", RowBox[List["6", " ", "a"]]]]], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["120", " ", SuperscriptBox["a", "5"]]], "+", RowBox[List[SuperscriptBox["a", "4"], " ", RowBox[List["(", RowBox[List["274", "+", RowBox[List["600", " ", "w"]]]], ")"]]]], "-", RowBox[List["3", " ", SuperscriptBox["a", "3"], " ", RowBox[List["(", RowBox[List["75", "+", RowBox[List["474", " ", "w"]], "+", RowBox[List["400", " ", SuperscriptBox["w", "2"]]]]], ")"]]]], "+", RowBox[List[SuperscriptBox["a", "2"], " ", RowBox[List["(", RowBox[List["85", "+", RowBox[List["3", " ", "w", " ", RowBox[List["(", RowBox[List["399", "+", RowBox[List["874", " ", "w"]], "+", RowBox[List["400", " ", SuperscriptBox["w", "2"]]]]], ")"]]]]]], ")"]]]], "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["57", "+", RowBox[List["2", " ", "w", " ", RowBox[List["(", RowBox[List["212", "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["437", "+", RowBox[List["60", " ", "w", " ", RowBox[List["(", RowBox[List["5", "+", "w"]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]], "-", RowBox[List["a", " ", RowBox[List["(", RowBox[List["15", "+", RowBox[List["2", " ", "w", " ", RowBox[List["(", RowBox[List["216", "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["923", "+", RowBox[List["w", " ", RowBox[List["(", RowBox[List["1037", "+", RowBox[List["300", " ", "w"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["Gamma", "[", "a", "]"]], "6"]]], "/;", RowBox[List["w", "\[Equal]", RowBox[List["InverseGammaRegularized", "[", RowBox[List["a", ",", "z"]], "]"]]]]]]]]]]










Date Added to functions.wolfram.com (modification date)





2007-05-02





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