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; }

 HypergeometricPFQ

 http://functions.wolfram.com/07.28.16.0001.01

 Input Form

 HypergeometricPFQ[{Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, c z] HypergeometricPFQ[{Subscript[\[Alpha], 1], Subscript[\[Alpha], 2], Subscript[\[Alpha], 3], Subscript[\[Alpha], 4]}, {Subscript[\[Beta], 1], Subscript[\[Beta], 2], Subscript[\[Beta], 3]}, d z] == Sum[Subscript[c, k] z^k, {k, 0, Infinity}] /; Subscript[c, k] == ((d^k Product[Pochhammer[Subscript[\[Alpha], j], k], {j, 1, 4}])/(k! Product[Pochhammer[Subscript[\[Beta], j], k], {j, 1, 3}])) HypergeometricPFQ[{-k, 1 - Subscript[\[Beta], 1] - k, 1 - Subscript[\[Beta], 2] - k, 1 - Subscript[\[Beta], 3] - k, Subscript[a, 1], Subscript[a, 2], Subscript[a, 3], Subscript[a, 4]}, {1 - Subscript[\[Alpha], 1] - k, 1 - Subscript[\[Alpha], 2] - k, 1 - Subscript[\[Alpha], 3] - k, 1 - Subscript[\[Alpha], 4] - k, Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, c/d] || Subscript[c, k] == ((c^k Product[Pochhammer[Subscript[a, j], k], {j, 1, 4}])/(k! Product[Pochhammer[Subscript[b, j], k], {j, 1, 3}])) HypergeometricPFQ[{-k, 1 - Subscript[b, 1] - k, 1 - Subscript[b, 2] - k, 1 - Subscript[b, 3] - k, Subscript[\[Alpha], 1], Subscript[\[Alpha], 2], Subscript[\[Alpha], 3], Subscript[\[Alpha], 4]}, {1 - Subscript[a, 1] - k, 1 - Subscript[a, 2] - k, 1 - Subscript[a, 3] - k, 1 - Subscript[a, 4] - k, Subscript[\[Beta], 1], Subscript[\[Beta], 2], Subscript[\[Beta], 3]}, d/c]

 Standard Form

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 MathML Form

 4 F 3 ( α 1 , α 2 , α 3 , α 4 ; β 1 , β 2 , β 3 ; d z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["4", TraditionalForm]], SubscriptBox["F", FormBox["3", 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]], ",", TagBox[SubscriptBox["\[Alpha]", "4"], 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]], ",", TagBox[SubscriptBox["\[Beta]", "3"], 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 c k z k /; c k d k j = 1 4 ( α j ) k TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["\[Alpha]", "j"], ")"]], "k"], Pochhammer] k ! j = 1 3 ( β j ) k TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["\[Beta]", "j"], ")"]], "k"], Pochhammer] 8 F 7 ( - k , 1 - k - β 1 , 1 - k - β 2 , 1 - k - β 3 , a 1 , a 2 , a 3 , a 4 ; 1 - k - α 1 , 1 - k - α 2 , 1 - k - α 3 , 1 - k - α 4 , b 1 , b 2 , b 3 ; c d ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["8", TraditionalForm]], SubscriptBox["F", FormBox["7", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", "k"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["\[Beta]", "1"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["\[Beta]", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["\[Beta]", "3"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["a", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["\[Alpha]", "1"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["\[Alpha]", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["\[Alpha]", "3"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["\[Alpha]", "4"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["b", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["c", "d"], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] c k c k j = 1 4 ( a j ) k TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["a", "j"], ")"]], "k"], Pochhammer] k ! j = 1 3 ( b j ) k TagBox[SubscriptBox[RowBox[List["(", SubscriptBox["b", "j"], ")"]], "k"], Pochhammer] 8 F 7 ( - k , 1 - k - b 1 , 1 - k - b 2 , 1 - k - b 3 , α 1 , α 2 , α 3 , α 4 ; 1 - k - a 1 , 1 - k - a 2 , 1 - k - a 3 , 1 - k - a 4 , β 1 , β 2 , β 3 ; d c ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", FormBox["8", TraditionalForm]], SubscriptBox["F", FormBox["7", TraditionalForm]]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List["-", "k"]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["b", "1"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["b", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["b", "3"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["\[Alpha]", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["\[Alpha]", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["\[Alpha]", "3"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["\[Alpha]", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["a", "1"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["a", "2"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["a", "3"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List["1", "-", "k", "-", SubscriptBox["a", "4"]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["\[Beta]", "1"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["\[Beta]", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[SubscriptBox["\[Beta]", "3"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[FractionBox["d", "c"], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] Condition HypergeometricPFQ Subscript α 1 Subscript α 2 Subscript α 3 Subscript α 4 Subscript β 1 Subscript β 2 Subscript β 3 d z k 0 Subscript c k z k Subscript c k d k j 1 4 Pochhammer Subscript α j k k j 1 3 Pochhammer Subscript β j k -1 HypergeometricPFQ -1 k 1 -1 k -1 Subscript β 1 1 -1 k -1 Subscript β 2 1 -1 k -1 Subscript β 3 Subscript a 1 Subscript a 2 Subscript a 3 Subscript a 4 1 -1 k -1 Subscript α 1 1 -1 k -1 Subscript α 2 1 -1 k -1 Subscript α 3 1 -1 k -1 Subscript α 4 Subscript b 1 Subscript b 2 Subscript b 3 c d -1 Subscript c k c k j 1 4 Pochhammer Subscript a j k k j 1 3 Pochhammer Subscript b j k -1 HypergeometricPFQ -1 k 1 -1 k -1 Subscript b 1 1 -1 k -1 Subscript b 2 1 -1 k -1 Subscript b 3 Subscript α 1 Subscript α 2 Subscript α 3 Subscript α 4 1 -1 k -1 Subscript a 1 1 -1 k -1 Subscript a 2 1 -1 k -1 Subscript a 3 1 -1 k -1 Subscript a 4 Subscript β 1 Subscript β 2 Subscript β 3 d c -1 [/itex]

 Rule Form

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

 2001-10-29