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 HypergeometricPFQ

 http://functions.wolfram.com/07.25.16.0002.01

 Input Form

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

 Standard Form

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 MathML Form

 2 F 2 ( a 1 , a 2 ; b 1 , b 2 ; c z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", 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]]]], 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] 2 F 2 ( α 1 , α 2 ; β 1 , β 2 ; d z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["2", 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]]]], 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 ( a 1 ) m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["a", "1"], ")"]], "m"], Pochhammer] ( a 2 ) m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["a", "2"], ")"]], "m"], Pochhammer] ( α 1 ) k - m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["\[Alpha]", "1"], ")"]], RowBox[List["k", "-", "m"]]], Pochhammer] ( α 2 ) k - m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["\[Alpha]", "2"], ")"]], RowBox[List["k", "-", "m"]]], Pochhammer] c m d k - m z k ( b 1 ) m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["b", "1"], ")"]], "m"], Pochhammer] ( b 2 ) m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["b", "2"], ")"]], "m"], Pochhammer] m ! ( β 1 ) k - m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["\[Beta]", "1"], ")"]], RowBox[List["k", "-", "m"]]], Pochhammer] ( β 2 ) k - m TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["\[Beta]", "2"], ")"]], RowBox[List["k", "-", "m"]]], Pochhammer] ( k - m ) ! HypergeometricPFQ Subscript a 1 Subscript a 2 Subscript b 1 Subscript b 2 c z HypergeometricPFQ Subscript α 1 Subscript α 2 Subscript β 1 Subscript β 2 d z m 0 k k 0 Pochhammer Subscript a 1 m Pochhammer Subscript a 2 m Pochhammer Subscript α 1 k -1 m Pochhammer Subscript α 2 k -1 m c m d k -1 m z k Pochhammer Subscript b 1 m Pochhammer Subscript b 2 m m Pochhammer Subscript β 1 k -1 m Pochhammer Subscript β 2 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