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 HypergeometricPFQ

 http://functions.wolfram.com/07.27.16.0002.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3]}, {Subscript[b, 1], Subscript[b, 2]}, c z] HypergeometricPFQ[{Subscript[\[Alpha], 1], Subscript[\[Alpha], 2], Subscript[\[Alpha], 3]}, {Subscript[\[Beta], 1], Subscript[\[Beta], 2]}, d z] == Sum[(Product[Pochhammer[Subscript[a, j], m] c^m, {j, 1, 3}]/ Product[Pochhammer[Subscript[b, j], m] m!, {j, 1, 2}]) (Product[Pochhammer[Subscript[\[Alpha], j], k - m] d^(k - m), {j, 1, 3}]/ Product[Pochhammer[Subscript[\[Beta], j], k - m] (k - m)!, {j, 1, 2}]) z^k, {k, 0, Infinity}, {m, 0, k}]

 Standard Form

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 MathML Form

 3 F 2 ( a 1 , a 2 , a 3 ; b 1 , b 2 ; c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["c", " ", "z"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] 3 F 2 ( α 1 , α 2 , α 3 ; β 1 , β 2 ; d z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["3", TraditionalForm]], SubscriptBox["F", FormBox["2", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["\[Alpha]", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["\[Alpha]", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["\[Alpha]", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[SubscriptBox["\[Beta]", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["\[Beta]", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["d", " ", "z"]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] k = 0 m = 0 k ( j = 1 3 ( a j ) m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["a", "j"], ")"]], "m"], Pochhammer] c m ) ( j = 1 3 ( α j ) k - m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["\[Alpha]", "j"], ")"]], RowBox[List["k", "-", "m"]]], Pochhammer] d k - m ) z k ( j = 1 2 ( b j ) m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["b", "j"], ")"]], "m"], Pochhammer] m ! ) j = 1 2 ( β j ) k - m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["\[Beta]", "j"], ")"]], RowBox[List["k", "-", "m"]]], Pochhammer] ( k - m ) ! HypergeometricPFQ Subscript a 1 Subscript a 2 Subscript a 3 Subscript b 1 Subscript b 2 c z HypergeometricPFQ Subscript α 1 Subscript α 2 Subscript α 3 Subscript β 1 Subscript β 2 d z m 0 k k 0 j 1 3 Pochhammer Subscript a j m c m j 1 3 Pochhammer Subscript α j k -1 m d k -1 m z k j 1 2 Pochhammer Subscript b j m m j 1 2 Pochhammer Subscript β j k -1 m k -1 m -1 [/itex]

 Rule Form

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

 2001-10-29