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; }

 KelvinKei

 http://functions.wolfram.com/03.19.06.0045.01

 Input Form

 KelvinKei[\[Nu], z] \[Proportional] (E^(-(((1 + I) z)/Sqrt[2]) + (Pi I (\[Nu] + 1))/2)/ (8 Sqrt[2 Pi] Sqrt[(-(-1)^(1/4)) z] ((-1)^(3/4) z)^(3/2))) ((Sqrt[(-(-1)^(1/4)) z] (Pi (4 (-1)^\[Nu] z - 3 I E^((1 + I) Sqrt[2] z) z + ((3 - 3 I) (-1)^\[Nu] Sqrt[I z^2])/Sqrt[2]) + 4 (E^((1 + I) Sqrt[2] z) z + (-1)^(1/4 + \[Nu]) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z])) - Sqrt[(-1)^(3/4) z] ((-(Pi/Sqrt[2])) (I Sqrt[2] E^(I Sqrt[2] z) z + (1 + I) (-1)^\[Nu] E^(Sqrt[2] z) ((-2 + 2 I) Sqrt[2] z + Sqrt[(-I) z^2])) + 4 (E^(I Sqrt[2] z) z - (-1)^(3/4 + \[Nu]) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z]))) HypergeometricPFQ[{(1 - 2 \[Nu])/8, (3 - 2 \[Nu])/8, (5 - 2 \[Nu])/8, (7 - 2 \[Nu])/8, (1 + 2 \[Nu])/8, (3 + 2 \[Nu])/8, (5 + 2 \[Nu])/8, (7 + 2 \[Nu])/8}, {1/4, 1/2, 3/4}, -(16/z^4)] - (((-1)^(3/4) (1 - 4 \[Nu]^2))/(8 z)) (Sqrt[(-(-1)^(1/4)) z] (Pi (-4 (-1)^\[Nu] z - 3 I E^((1 + I) Sqrt[2] z) z + 3 (-1)^(3/4 + \[Nu]) Sqrt[I z^2]) + 4 (E^((1 + I) Sqrt[2] z) z - (-1)^(1/4 + \[Nu]) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z])) - Sqrt[(-1)^(3/4) z] ((1/2) (-2 E^(I Sqrt[2] z) Pi z + (1 + I) (-1)^\[Nu] E^(Sqrt[2] z) Pi ((4 + 4 I) z - I Sqrt[2] Sqrt[(-I) z^2])) + 4 ((-I) E^(I Sqrt[2] z) z + (-1)^(1/4 + \[Nu]) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z]))) HypergeometricPFQ[{(3 - 2 \[Nu])/8, (5 - 2 \[Nu])/8, (7 - 2 \[Nu])/8, (9 - 2 \[Nu])/8, (3 + 2 \[Nu])/8, (5 + 2 \[Nu])/8, (7 + 2 \[Nu])/8, (9 + 2 \[Nu])/8}, {1/2, 3/4, 5/4}, -(16/z^4)] - ((I (9 - 40 \[Nu]^2 + 16 \[Nu]^4))/(128 z^2)) (Sqrt[(-(-1)^(1/4)) z] (Pi (4 (-1)^\[Nu] z - 3 I E^((1 + I) Sqrt[2] z) z + ((3 - 3 I) (-1)^\[Nu] Sqrt[I z^2])/Sqrt[2]) + 4 (E^((1 + I) Sqrt[2] z) z + (-1)^(1/4 + \[Nu]) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z])) + Sqrt[(-1)^(3/4) z] ((-(Pi/Sqrt[2])) (I Sqrt[2] E^(I Sqrt[2] z) z + (1 + I) (-1)^\[Nu] E^(Sqrt[2] z) ((-2 + 2 I) Sqrt[2] z + Sqrt[(-I) z^2])) + 4 (E^(I Sqrt[2] z) z - (-1)^(3/4 + \[Nu]) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z]))) HypergeometricPFQ[{(5 - 2 \[Nu])/8, (7 - 2 \[Nu])/8, (9 - 2 \[Nu])/8, (11 - 2 \[Nu])/8, (5 + 2 \[Nu])/8, (7 + 2 \[Nu])/8, (9 + 2 \[Nu])/8, (11 + 2 \[Nu])/8}, {3/4, 5/4, 3/2}, -(16/z^4)] + (((-1)^(1/4) (-225 + 1036 \[Nu]^2 - 560 \[Nu]^4 + 64 \[Nu]^6))/ (3072 z^3)) (Sqrt[(-(-1)^(1/4)) z] (Pi (-4 (-1)^\[Nu] z - 3 I E^((1 + I) Sqrt[2] z) z + 3 (-1)^(3/4 + \[Nu]) Sqrt[I z^2]) + 4 (E^((1 + I) Sqrt[2] z) z - (-1)^(1/4 + \[Nu]) Sqrt[I z^2]) (-Log[z] + Log[(-1)^(3/4) z])) + Sqrt[(-1)^(3/4) z] ((1/2) (-2 E^(I Sqrt[2] z) Pi z + (1 + I) (-1)^\[Nu] E^(Sqrt[2] z) Pi ((4 + 4 I) z - I Sqrt[2] Sqrt[(-I) z^2])) + 4 ((-I) E^(I Sqrt[2] z) z + (-1)^(1/4 + \[Nu]) E^(Sqrt[2] z) Sqrt[(-I) z^2]) (-Log[z] + Log[(-(-1)^(1/4)) z]))) HypergeometricPFQ[ {(7 - 2 \[Nu])/8, (9 - 2 \[Nu])/8, (11 - 2 \[Nu])/8, (13 - 2 \[Nu])/8, (7 + 2 \[Nu])/8, (9 + 2 \[Nu])/8, (11 + 2 \[Nu])/8, (13 + 2 \[Nu])/8}, {5/4, 3/2, 7/4}, -(16/z^4)]) /; (Abs[z] -> Infinity) && Element[\[Nu], Integers]

 Standard Form

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SuperscriptBox["z", "4"]]]]]], "]"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "\[And]", RowBox[List["\[Nu]", "\[Element]", "Integers"]]]]]]]]

 MathML Form

 kei ν ( z ) π ( ν + 1 ) 2 - ( 1 + ) z 2 8 2 π - - 1 4 z ( ( - 1 ) 3 / 4 z ) 3 / 2 ( ( - ( - 1 ) 3 / 4 z ( 4 ( 2 z z - ( - 1 ) ν + 3 4 2 z - z 2 ) ( log ( - - 1 4 z ) - log ( z ) ) - π 2 ( 2 2 z z + ( - 1 ) ν 2 z ( 1 + ) ( 2 ( - 2 + 2 ) z + - z 2 ) ) ) + - - 1 4 z ( π ( ( - 1 ) ν z 2 ( 3 - 3 ) 2 - 3 ( 1 + ) 2 z z + 4 ( - 1 ) ν z ) + 4 ( ( 1 + ) 2 z z + ( - 1 ) ν + 1 4 z 2 ) ( log ( ( - 1 ) 3 / 4 z ) - log ( z ) ) ) ) 8 F 3 ( 1 8 ( 1 - 2 ν ) , 1 8 ( 3 - 2 ν ) , 1 8 ( 5 - 2 ν ) , 1 8 ( 7 - 2 ν ) , 1 8 ( 2 ν + 1 ) , 1 8 ( 2 ν + 3 ) , 1 8 ( 2 ν + 5 ) , 1 8 ( 2 ν + 7 ) ; 1 4 , 1 2 , 3 4 ; - 16 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "1"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "3"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "5"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "7"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] - ( - 1 ) 3 / 4 ( 1 - 4 ν 2 ) 8 z ( - - 1 4 z ( π ( - 3 ( 1 + ) 2 z z - 4 ( - 1 ) ν z + 3 ( - 1 ) ν + 3 4 z 2 ) + 4 ( ( 1 + ) 2 z z - ( - 1 ) ν + 1 4 z 2 ) ( log ( ( - 1 ) 3 / 4 z ) - log ( z ) ) ) - ( - 1 ) 3 / 4 z ( 1 2 ( ( 1 + ) ( - 1 ) ν 2 z π ( ( 4 + 4 ) z - 2 - z 2 ) - 2 2 z π z ) + 4 ( ( - 1 ) ν + 1 4 2 z - z 2 - 2 z z ) ( log ( - - 1 4 z ) - log ( z ) ) ) ) 8 F 3 ( 1 8 ( 3 - 2 ν ) , 1 8 ( 5 - 2 ν ) , 1 8 ( 7 - 2 ν ) , 1 8 ( 9 - 2 ν ) , 1 8 ( 2 ν + 3 ) , 1 8 ( 2 ν + 5 ) , 1 8 ( 2 ν + 7 ) , 1 8 ( 2 ν + 9 ) ; 1 2 , 3 4 , 5 4 ; - 16 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "3"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "5"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "7"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "9"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["1", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - ( 16 ν 4 - 40 ν 2 + 9 ) 128 z 2 ( ( - 1 ) 3 / 4 z ( 4 ( 2 z z - ( - 1 ) ν + 3 4 2 z - z 2 ) ( log ( - - 1 4 z ) - log ( z ) ) - π 2 ( 2 2 z z + ( - 1 ) ν 2 z ( 1 + ) ( 2 ( - 2 + 2 ) z + - z 2 ) ) ) + - - 1 4 z ( π ( ( - 1 ) ν z 2 ( 3 - 3 ) 2 - 3 ( 1 + ) 2 z z + 4 ( - 1 ) ν z ) + 4 ( ( 1 + ) 2 z z + ( - 1 ) ν + 1 4 z 2 ) ( log ( ( - 1 ) 3 / 4 z ) - log ( z ) ) ) ) 8 F 3 ( 1 8 ( 5 - 2 ν ) , 1 8 ( 7 - 2 ν ) , 1 8 ( 9 - 2 ν ) , 1 8 ( 11 - 2 ν ) , 1 8 ( 2 ν + 5 ) , 1 8 ( 2 ν + 7 ) , 1 8 ( 2 ν + 9 ) , 1 8 ( 2 ν + 11 ) ; 3 4 , 5 4 , 3 2 ; - 16 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["5", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["11", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "5"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "7"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "9"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "11"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] + - 1 4 ( 64 ν 6 - 560 ν 4 + 1036 ν 2 - 225 ) 3072 z 3 ( ( - 1 ) 3 / 4 z ( 1 2 ( ( 1 + ) ( - 1 ) ν 2 z π ( ( 4 + 4 ) z - 2 - z 2 ) - 2 2 z π z ) + 4 ( ( - 1 ) ν + 1 4 2 z - z 2 - 2 z z ) ( log ( - - 1 4 z ) - log ( z ) ) ) + - - 1 4 z ( π ( - 3 ( 1 + ) 2 z z - 4 ( - 1 ) ν z + 3 ( - 1 ) ν + 3 4 z 2 ) + 4 ( ( 1 + ) 2 z z - ( - 1 ) ν + 1 4 z 2 ) ( log ( ( - 1 ) 3 / 4 z ) - log ( z ) ) ) ) 8 F 3 ( 1 8 ( 7 - 2 ν ) , 1 8 ( 9 - 2 ν ) , 1 8 ( 11 - 2 ν ) , 1 8 ( 13 - 2 ν ) , 1 8 ( 2 ν + 7 ) , 1 8 ( 2 ν + 9 ) , 1 8 ( 2 ν + 11 ) , 1 8 ( 2 ν + 13 ) ; 5 4 , 3 2 , 7 4 ; - 16 z 4 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "8"], SubscriptBox["F", "3"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["7", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["9", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["11", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List["13", "-", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "7"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "9"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "11"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[RowBox[List[FractionBox["1", "8"], " ", RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Nu]"]], "+", "13"]], ")"]]]], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[TagBox[RowBox[List[TagBox[FractionBox["5", "4"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["3", "2"], HypergeometricPFQ, Rule[Editable, True]], ",", TagBox[FractionBox["7", "4"], HypergeometricPFQ, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False]], ";", TagBox[RowBox[List["-", FractionBox["16", SuperscriptBox["z", "4"]]]], HypergeometricPFQ, Rule[Editable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False]], HypergeometricPFQ] ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) ν TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] Condition Proportional KelvinKei ν z ν 1 2 -1 -1 1 z 2 1 2 -1 8 2 1 2 -1 -1 1 4 z 1 2 -1 3 4 z 3 2 -1 -1 -1 3 4 z 1 2 4 2 1 2 z z -1 -1 ν 3 4 2 1 2 z -1 z 2 1 2 -1 -1 1 4 z -1 z -1 2 1 2 -1 2 1 2 2 1 2 z z -1 ν 2 1 2 z 1 2 1 2 -2 2 z -1 z 2 1 2 -1 -1 1 4 z 1 2 -1 ν z 2 1 2 3 -3 2 1 2 -1 -1 3 1 2 1 2 z z 4 -1 ν z 4 1 2 1 2 z z -1 ν 1 4 z 2 1 2 -1 3 4 z -1 z HypergeometricPFQ 1 8 1 -1 2 ν 1 8 3 -1 2 ν 1 8 5 -1 2 ν 1 8 7 -1 2 ν 1 8 2 ν 1 1 8 2 ν 3 1 8 2 ν 5 1 8 2 ν 7 1 4 1 2 3 4 -1 16 z 4 -1 -1 -1 3 4 1 -1 4 ν 2 8 z -1 -1 -1 1 4 z 1 2 -3 1 2 1 2 z z -1 4 -1 ν z 3 -1 ν 3 4 z 2 1 2 4 1 2 1 2 z z -1 -1 ν 1 4 z 2 1 2 -1 3 4 z -1 z -1 -1 3 4 z 1 2 1 2 1 -1 ν 2 1 2 z 4 4 z -1 2 1 2 -1 z 2 1 2 -1 2 2 1 2 z z 4 -1 ν 1 4 2 1 2 z -1 z 2 1 2 -1 2 1 2 z z -1 -1 1 4 z -1 z HypergeometricPFQ 1 8 3 -1 2 ν 1 8 5 -1 2 ν 1 8 7 -1 2 ν 1 8 9 -1 2 ν 1 8 2 ν 3 1 8 2 ν 5 1 8 2 ν 7 1 8 2 ν 9 1 2 3 4 5 4 -1 16 z 4 -1 -1 16 ν 4 -1 40 ν 2 9 128 z 2 -1 -1 3 4 z 1 2 4 2 1 2 z z -1 -1 ν 3 4 2 1 2 z -1 z 2 1 2 -1 -1 1 4 z -1 z -1 2 1 2 -1 2 1 2 2 1 2 z z -1 ν 2 1 2 z 1 2 1 2 -2 2 z -1 z 2 1 2 -1 -1 1 4 z 1 2 -1 ν z 2 1 2 3 -3 2 1 2 -1 -1 3 1 2 1 2 z z 4 -1 ν z 4 1 2 1 2 z z -1 ν 1 4 z 2 1 2 -1 3 4 z -1 z HypergeometricPFQ 1 8 5 -1 2 ν 1 8 7 -1 2 ν 1 8 9 -1 2 ν 1 8 11 -1 2 ν 1 8 2 ν 5 1 8 2 ν 7 1 8 2 ν 9 1 8 2 ν 11 3 4 5 4 3 2 -1 16 z 4 -1 -1 1 4 64 ν 6 -1 560 ν 4 1036 ν 2 -225 3072 z 3 -1 -1 3 4 z 1 2 1 2 1 -1 ν 2 1 2 z 4 4 z -1 2 1 2 -1 z 2 1 2 -1 2 2 1 2 z z 4 -1 ν 1 4 2 1 2 z -1 z 2 1 2 -1 2 1 2 z z -1 -1 1 4 z -1 z -1 -1 1 4 z 1 2 -3 1 2 1 2 z z -1 4 -1 ν z 3 -1 ν 3 4 z 2 1 2 4 1 2 1 2 z z -1 -1 ν 1 4 z 2 1 2 -1 3 4 z -1 z HypergeometricPFQ 1 8 7 -1 2 ν 1 8 9 -1 2 ν 1 8 11 -1 2 ν 1 8 13 -1 2 ν 1 8 2 ν 7 1 8 2 ν 9 1 8 2 ν 11 1 8 2 ν 13 5 4 3 2 7 4 -1 16 z 4 -1 Rule z ν [/itex]

 Rule Form

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

 2007-05-02