html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 MeijerG

 http://functions.wolfram.com/07.34.03.0555.01

 Input Form

 MeijerG[{{a, c, 2 a - c + 1}, {}}, {{b}, {-(1/2) + a, 2 a - b}}, z] == (2^(1 + 2 a - 2 b) Sqrt[Pi] z^b Gamma[1 + b - c] Gamma[-2 a + b + c] ((-(-2 a + b + c)) Hypergeometric2F1[(1/2) (1 + b - c), (1/2) (1 - 2 a + b + c), 1/2 - a + b, -z] Hypergeometric2F1[ (1/2) (1 + b - c), (1/2) (1 - 2 a + b + c), 3/2 - a + b, -z] + (1 + b - c) Hypergeometric2F1[(1/2) (2 + b - c), (1/2) (-2 a + b + c), 1/2 - a + b, -z] Hypergeometric2F1[(1/2) (2 + b - c), (1/2) (-2 a + b + c), 3/2 - a + b, -z]))/ ((1 - 2 a + 2 b) (1 + 2 a - 2 c) Gamma[1/2 - a + b]^2)

 Standard Form

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 MathML Form

 G 3 , 3 1 , 3 ( z a , c , 2 a - c + 1 b , a - 1 2 , 2 a - b ) TagBox[RowBox[List[SubsuperscriptBox[TagBox["G", MeijerG], RowBox[List["3", ",", "3"]], RowBox[List["1", ",", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox["z", MeijerG, Rule[Editable, True]], "\[VerticalSeparator]", GridBox[List[List[RowBox[List[TagBox["a", MeijerG, Rule[Editable, True]], ",", TagBox["c", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "c", "+", "1"]], MeijerG, Rule[Editable, True]]]]], List[RowBox[List[TagBox["b", MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List["a", "-", FractionBox["1", "2"]]], MeijerG, Rule[Editable, True]], ",", TagBox[RowBox[List[RowBox[List["2", " ", "a"]], "-", "b"]], MeijerG, Rule[Editable, True]]]]]]]]], ")"]]]], MeijerG, Rule[Editable, False]] 2 2 a - 2 b + 1 π Γ ( b - c + 1 ) Γ ( b + c - 2 a ) ( 2 b - 2 a + 1 ) ( 2 a - 2 c + 1 ) Γ ( b - a + 1 2 ) 2 z b ( ( b - c + 1 ) 2 F 1 ( b - c 2 + 1 , b + c 2 - a ; b - a + 1 2 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List["b", "-", "c"]], "2"], " ", "+", "1"]], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox[RowBox[List["b", "+", "c"]], "2"], " ", "-", "a"]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["b", "-", "a", "+", FractionBox["1", "2"]]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[RowBox[List["-", "z"]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] 2 F 1 ( b - c 2 + 1 , b + c 2 - a ; b - a + 3 2 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox[RowBox[List["b", "-", "c"]], "2"], " ", "+", "1"]], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["b", "+", "c"]], "2"], " ", "-", "a"]], Hypergeometric2F1, Rule[Editable, True]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["b", "-", "a", "+", FractionBox["3", "2"]]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[RowBox[List["-", "z"]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] - ( b + c - 2 a ) 2 F 1 ( b - c + 1 2 , b + c + 1 2 - a ; b - a + 1 2 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["b", "-", "c", "+", "1"]], "2"], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["b", "+", "c", "+", "1"]], "2"], " ", "-", "a"]], Hypergeometric2F1, Rule[Editable, True]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["b", "-", "a", "+", FractionBox["1", "2"]]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[RowBox[List["-", "z"]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] 2 F 1 ( b - c + 1 2 , b + c + 1 2 - a ; b - a + 3 2 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", TraditionalForm]], SubscriptBox["F", FormBox["1", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[RowBox[List["b", "-", "c", "+", "1"]], "2"], Hypergeometric2F1, Rule[Editable, True]], ",", TagBox[TagBox[RowBox[List[FractionBox[RowBox[List["b", "+", "c", "+", "1"]], "2"], " ", "-", "a"]], Hypergeometric2F1, Rule[Editable, True]], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[TagBox[TagBox[RowBox[List["b", "-", "a", "+", FractionBox["3", "2"]]], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], ";", TagBox[RowBox[List["-", "z"]], Hypergeometric2F1, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], Hypergeometric2F1] ) MeijerG a c 2 a -1 c 1 b a -1 1 2 2 a -1 b z 2 2 a -1 2 b 1 1 2 Gamma b -1 c 1 Gamma b c -1 2 a 2 b -1 2 a 1 2 a -1 2 c 1 Gamma b -1 a 1 2 2 -1 z b b -1 c 1 Hypergeometric2F1 b -1 c 2 -1 1 b c 2 -1 -1 a b -1 a 1 2 -1 z Hypergeometric2F1 b -1 c 2 -1 1 Hypergeometric2F1 b c 2 -1 -1 a b -1 a 3 2 -1 z -1 b c -1 2 a Hypergeometric2F1 b -1 c 1 2 -1 Hypergeometric2F1 b c 1 2 -1 -1 a b -1 a 1 2 -1 z Hypergeometric2F1 b -1 c 1 2 -1 Hypergeometric2F1 b c 1 2 -1 -1 a b -1 a 3 2 -1 z [/itex]

 Rule Form

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

 2001-10-29