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variants of this functions
MeijerG




Mathematica Notation

Traditional Notation









Hypergeometric Functions > MeijerG[{{a1,...,an},{an+1,...,ap}},{{b1,...,bm},{bm+1,...,bq}},z] > Specific values > Specialized values > Cases with m==2 > Case {m,n,p,q}={2,0,2,3}





http://functions.wolfram.com/07.34.03.0716.01









  


  








Input Form





MeijerG[{{}, {Subscript[a, 1], Subscript[a, 2]}}, {{Subscript[b, 1], Subscript[b, 2]}, {Subscript[b, 3]}}, z] == Pi Csc[Pi (-Subscript[b, 1] + Subscript[b, 2])] ((z^Subscript[b, 1]/(Gamma[Subscript[a, 1] - Subscript[b, 1]] Gamma[Subscript[a, 2] - Subscript[b, 1]])) HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 1], 1 - Subscript[a, 2] + Subscript[b, 1]}, {1 + Subscript[b, 1] - Subscript[b, 2], 1 + Subscript[b, 1] - Subscript[b, 3]}, z] - (z^Subscript[b, 2]/(Gamma[Subscript[a, 1] - Subscript[b, 2]] Gamma[Subscript[a, 2] - Subscript[b, 2]])) HypergeometricPFQRegularized[{1 - Subscript[a, 1] + Subscript[b, 2], 1 - Subscript[a, 2] + Subscript[b, 2]}, {1 - Subscript[b, 1] + Subscript[b, 2], 1 + Subscript[b, 2] - Subscript[b, 3]}, z]) /; !Element[Subscript[b, 2] - Subscript[b, 1], Integers]








Standard Form





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MathML Form







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<apply> <notin /> <apply> <plus /> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <ci> Subscript </ci> <ci> b </ci> <cn type='integer'> 1 </cn> </apply> </apply> </apply> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[SubscriptBox["a_", "1"], ",", SubscriptBox["a_", "2"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[SubscriptBox["b_", "1"], ",", SubscriptBox["b_", "2"]]], "}"]], ",", RowBox[List["{", SubscriptBox["b_", "3"], "}"]]]], "}"]], ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["\[Pi]", " ", RowBox[List["Csc", "[", RowBox[List["\[Pi]", " ", RowBox[List["(", RowBox[List[RowBox[List["-", SubscriptBox["bb", "1"]]], "+", SubscriptBox["bb", "2"]]], ")"]]]], "]"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", SubscriptBox["bb", "1"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["aa", "1"], "+", SubscriptBox["bb", "1"]]], ",", RowBox[List["1", "-", SubscriptBox["aa", "2"], "+", SubscriptBox["bb", "1"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "+", SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["bb", "1"], "-", SubscriptBox["bb", "3"]]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["aa", "1"], "-", SubscriptBox["bb", "1"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["aa", "2"], "-", SubscriptBox["bb", "1"]]], "]"]]]]], "-", FractionBox[RowBox[List[SuperscriptBox["z", SubscriptBox["bb", "2"]], " ", RowBox[List["HypergeometricPFQRegularized", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["aa", "1"], "+", SubscriptBox["bb", "2"]]], ",", RowBox[List["1", "-", SubscriptBox["aa", "2"], "+", SubscriptBox["bb", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", SubscriptBox["bb", "1"], "+", SubscriptBox["bb", "2"]]], ",", RowBox[List["1", "+", SubscriptBox["bb", "2"], "-", SubscriptBox["bb", "3"]]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["aa", "1"], "-", SubscriptBox["bb", "2"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[SubscriptBox["aa", "2"], "-", SubscriptBox["bb", "2"]]], "]"]]]]]]], ")"]]]], "/;", RowBox[List["!", RowBox[List[RowBox[List[SubscriptBox["bb", "2"], "-", SubscriptBox["bb", "1"]]], "\[Element]", "Integers"]]]]]]]]]]


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





2001-10-29