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 KelvinBer

 http://functions.wolfram.com/03.18.17.0004.01

 Input Form

 KelvinBer[\[Nu], z] == (2/z)^(-1 + n) Pochhammer[1 - \[Nu], -1 + n] HypergeometricPFQ[{1/4 - n/4, 1/2 - n/4, 3/4 - n/4, 1 - n/4}, {1/2, 1/2 - n/2, 1 - n/2, 1/2 - \[Nu]/2, 1 - \[Nu]/2, 1/2 - n/2 + \[Nu]/2, 1 - n/2 + \[Nu]/2}, -(z^4/16)] ((-KelvinBer[-1 - n + \[Nu], z]) Sin[(1/4) (1 + n) Pi] - KelvinBei[-1 - n + \[Nu], z] Cos[(1/4) (1 + n) Pi]) - (1/(1 - \[Nu])) Pochhammer[1 - \[Nu], n - 2] (-2 + n) (2/z)^(-3 + n) HypergeometricPFQ[{3/4 - n/4, 1 - n/4, 5/4 - n/4, 3/2 - n/4}, {3/2, 1 - n/2, 3/2 - n/2, 1 - \[Nu]/2, 3/2 - \[Nu]/2, 1 - n/2 + \[Nu]/2, 3/2 - n/2 + \[Nu]/2}, -(z^4/16)] (KelvinBer[-1 - n + \[Nu], z] Cos[(1/4) (1 + n) Pi] - KelvinBei[-1 - n + \[Nu], z] Sin[(1/4) (1 + n) Pi]) - Pochhammer[2 - \[Nu], n - 2] (-1 + n) (2/z)^(-2 + n) HypergeometricPFQ[{1/2 - n/4, 3/4 - n/4, 1 - n/4, 5/4 - n/4}, {3/2, 1/2 - n/2, 1 - n/2, 1 - \[Nu]/2, 3/2 - \[Nu]/2, 1/2 - n/2 + \[Nu]/2, 1 - n/2 + \[Nu]/2}, -(z^4/16)] (KelvinBei[-n + \[Nu], z] Cos[(n Pi)/4] + KelvinBer[-n + \[Nu], z] Sin[(n Pi)/4]) + Pochhammer[1 - \[Nu], n] (2/z)^n HypergeometricPFQ[{1/4 - n/4, 1/2 - n/4, 3/4 - n/4, -(n/4)}, {1/2, 1/2 - n/2, -(n/2), 1/2 - \[Nu]/2, 1 - \[Nu]/2, -(n/2) + \[Nu]/2, 1/2 - n/2 + \[Nu]/2}, -(z^4/16)] (KelvinBer[-n + \[Nu], z] Cos[(n Pi)/4] - KelvinBei[-n + \[Nu], z] Sin[(n Pi)/4]) /; Element[n, Integers] && n >= 3

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List[SuperscriptBox[RowBox[List["(", FractionBox["2", "z"], ")"]], RowBox[List[RowBox[List["-", "1"]], "+", "n"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", RowBox[List[RowBox[List["-", "1"]], "+", "n"]]]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], "-", FractionBox["n", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "-", FractionBox["n", "4"]]], ",", RowBox[List["1", "-", FractionBox["n", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "2"]]], ",", RowBox[List["1", "-", FractionBox["n", "2"]]], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "-", FractionBox["n", "2"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "16"]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", RowBox[List["KelvinBer", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "-", "n", "+", "\[Nu]"]], ",", "z"]], "]"]]]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]], " ", "\[Pi]"]], "]"]]]], "-", RowBox[List[RowBox[List["KelvinBei", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "-", "n", "+", "\[Nu]"]], ",", "z"]], "]"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]], " ", "\[Pi]"]], "]"]]]]]], ")"]]]], "-", RowBox[List[FractionBox["1", RowBox[List["1", "-", "\[Nu]"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", RowBox[List["n", "-", "2"]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "2"]], "+", "n"]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["2", "z"], ")"]], RowBox[List[RowBox[List["-", "3"]], "+", "n"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["3", "4"], "-", FractionBox["n", "4"]]], ",", RowBox[List["1", "-", FractionBox["n", "4"]]], ",", RowBox[List[FractionBox["5", "4"], "-", FractionBox["n", "4"]]], ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["n", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List["1", "-", FractionBox["n", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["n", "2"]]], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "-", FractionBox["n", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["n", "2"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "16"]]]]], "]"]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["KelvinBer", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "-", "n", "+", "\[Nu]"]], ",", "z"]], "]"]], " ", RowBox[List["Cos", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]], " ", "\[Pi]"]], "]"]]]], "-", RowBox[List[RowBox[List["KelvinBei", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "-", "n", "+", "\[Nu]"]], ",", "z"]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", "n"]], ")"]], " ", "\[Pi]"]], "]"]]]]]], ")"]]]], "-", " ", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["2", "-", "\[Nu]"]], ",", RowBox[List["n", "-", "2"]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List["-", "1"]], "+", "n"]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["2", "z"], ")"]], RowBox[List[RowBox[List["-", "2"]], "+", "n"]]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "-", FractionBox["n", "4"]]], ",", RowBox[List["1", "-", FractionBox["n", "4"]]], ",", RowBox[List[FractionBox["5", "4"], "-", FractionBox["n", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["3", "2"], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "2"]]], ",", RowBox[List["1", "-", FractionBox["n", "2"]]], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "2"], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "-", FractionBox["n", "2"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "16"]]]]], "]"]], RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["KelvinBei", "[", RowBox[List[RowBox[List[RowBox[List["-", "n"]], "+", "\[Nu]"]], ",", "z"]], "]"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["n", " ", "\[Pi]"]], "4"], "]"]]]], "+", RowBox[List[RowBox[List["KelvinBer", "[", RowBox[List[RowBox[List[RowBox[List["-", "n"]], "+", "\[Nu]"]], ",", "z"]], "]"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["n", " ", "\[Pi]"]], "4"], "]"]]]]]], ")"]]]], "+", RowBox[List[RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]"]], ",", "n"]], "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["2", "z"], ")"]], "n"], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], "-", FractionBox["n", "4"]]], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "4"]]], ",", RowBox[List[FractionBox["3", "4"], "-", FractionBox["n", "4"]]], ",", RowBox[List["-", FractionBox["n", "4"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "2"]]], ",", RowBox[List["-", FractionBox["n", "2"]]], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "2"], "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "16"]]]]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["KelvinBer", "[", RowBox[List[RowBox[List[RowBox[List["-", "n"]], "+", "\[Nu]"]], ",", "z"]], "]"]], " ", RowBox[List["Cos", "[", FractionBox[RowBox[List["n", " ", "\[Pi]"]], "4"], "]"]]]], "-", RowBox[List[RowBox[List["KelvinBei", "[", RowBox[List[RowBox[List[RowBox[List["-", "n"]], "+", "\[Nu]"]], ",", "z"]], "]"]], " ", RowBox[List["Sin", "[", FractionBox[RowBox[List["n", " ", "\[Pi]"]], "4"], "]"]]]]]], ")"]]]]]]]], "/;", RowBox[List[RowBox[List["Element", "[", RowBox[List["n", ",", "Integers"]], "]"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "3"]]]]]]]]

 MathML Form

 ber ν ( z ) - ( 2 - ν ) n - 2 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["2", "-", "\[Nu]"]], ")"]], RowBox[List["n", "-", "2"]]], Pochhammer] ( n - 1 ) ( 2 z ) n - 2 4 F 7 ( 1 2 - n 4 , 3 4 - n 4 , 1 - n 4 , 5 4 - n 4 ; 3 2 , 1 2 - n 2 , 1 - n 2 , 1 - ν 2 , 3 2 - ν 2 , - n 2 + ν 2 + 1 2 , - n 2 + ν 2 + 1 ; - z 4 16 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "7"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["3", "4"], "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["5", "4"], "-", FractionBox["n", "4"]]], 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["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], "+", FractionBox["\[Nu]", "2"], "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], "+", FractionBox["\[Nu]", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "16"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] ( cos ( n π 4 ) bei ν - n ( z ) + ber ν - n ( z ) sin ( n π 4 ) ) + ( 1 - ν ) n - 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["1", "-", "\[Nu]"]], ")"]], RowBox[List["n", "-", "1"]]], Pochhammer] ( 2 z ) n - 1 4 F 7 ( 1 4 - n 4 , 1 2 - n 4 , 3 4 - n 4 , 1 - n 4 ; 1 2 , 1 2 - n 2 , 1 - n 2 , 1 2 - ν 2 , 1 - ν 2 , - n 2 + ν 2 + 1 2 , - n 2 + ν 2 + 1 ; - z 4 16 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "7"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "4"], "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["3", "4"], "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["n", "4"]]], 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[RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], "+", FractionBox["\[Nu]", "2"], "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], "+", FractionBox["\[Nu]", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "16"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] ( - cos ( 1 4 ( n + 1 ) π ) bei - n + ν - 1 ( z ) - ber - n + ν - 1 ( z ) sin ( 1 4 ( n + 1 ) π ) ) + ( 1 - ν ) n TagBox[SubscriptBox[RowBox[List["(", RowBox[List["1", "-", "\[Nu]"]], ")"]], "n"], Pochhammer] ( 2 z ) n 4 F 7 ( 1 4 - n 4 , 1 2 - n 4 , 3 4 - n 4 , - n 4 ; 1 2 , 1 2 - n 2 , - n 2 , 1 2 - ν 2 , 1 - ν 2 , ν 2 - n 2 , - n 2 + ν 2 + 1 2 ; - z 4 16 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "7"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["1", "4"], "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["3", "4"], "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["n", "4"]]], 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[RowBox[List[FractionBox["1", "2"], "-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["1", "2"], "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["\[Nu]", "2"], "-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], "+", FractionBox["\[Nu]", "2"], "+", FractionBox["1", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "16"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] ( ber ν - n ( z ) cos ( n π 4 ) - bei ν - n ( z ) sin ( n π 4 ) ) - ( 1 - ν ) n - 2 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["1", "-", "\[Nu]"]], ")"]], RowBox[List["n", "-", "2"]]], Pochhammer] ( n - 2 ) 1 - ν ( 2 z ) n - 3 4 F 7 ( 3 4 - n 4 , 1 - n 4 , 5 4 - n 4 , 3 2 - n 4 ; 3 2 , 1 - n 2 , 3 2 - n 2 , 1 - ν 2 , 3 2 - ν 2 , - n 2 + ν 2 + 1 , - n 2 + ν 2 + 3 2 ; - z 4 16 ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "4"], SubscriptBox["F", "7"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[RowBox[List[FractionBox["3", "4"], "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["5", "4"], "-", FractionBox["n", "4"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["3", "2"], "-", FractionBox["n", "4"]]], 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["3", "2"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["3", "2"], "-", FractionBox["n", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List["1", "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[FractionBox["3", "2"], "-", FractionBox["\[Nu]", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], "+", FractionBox["\[Nu]", "2"], "+", "1"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox[RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], "+", FractionBox["\[Nu]", "2"], "+", FractionBox["3", "2"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", FractionBox[SuperscriptBox["z", "4"], "16"]]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] ( ber - n + ν - 1 ( z ) cos ( 1 4 ( n + 1 ) π ) - bei - n + ν - 1 ( z ) sin ( 1 4 ( n + 1 ) π ) ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[List[], Integers]] n 3 Condition KelvinBer ν z -1 Pochhammer 2 -1 ν n -2 n -1 2 z -1 n -2 HypergeometricPFQ 1 2 -1 n 4 -1 3 4 -1 n 4 -1 1 -1 n 4 -1 5 4 -1 n 4 -1 3 2 1 2 -1 n 2 -1 1 -1 n 2 -1 1 -1 ν 2 -1 3 2 -1 ν 2 -1 -1 n 2 -1 ν 2 -1 1 2 -1 n 2 -1 ν 2 -1 1 -1 z 4 16 -1 n 4 -1 KelvinBei ν -1 n z KelvinBer ν -1 n z sin n 4 -1 Pochhammer 1 -1 ν n -1 2 z -1 n -1 HypergeometricPFQ 1 4 -1 n 4 -1 1 2 -1 n 4 -1 3 4 -1 n 4 -1 1 -1 n 4 -1 1 2 1 2 -1 n 2 -1 1 -1 n 2 -1 1 2 -1 ν 2 -1 1 -1 ν 2 -1 -1 n 2 -1 ν 2 -1 1 2 -1 n 2 -1 ν 2 -1 1 -1 z 4 16 -1 -1 1 4 n 1 KelvinBei -1 n ν -1 z -1 KelvinBer -1 n ν -1 z 1 4 n 1 Pochhammer 1 -1 ν n 2 z -1 n HypergeometricPFQ 1 4 -1 n 4 -1 1 2 -1 n 4 -1 3 4 -1 n 4 -1 -1 n 4 -1 1 2 1 2 -1 n 2 -1 -1 n 2 -1 1 2 -1 ν 2 -1 1 -1 ν 2 -1 ν 2 -1 -1 n 2 -1 -1 n 2 -1 ν 2 -1 1 2 -1 z 4 16 -1 KelvinBer ν -1 n z n 4 -1 -1 KelvinBei ν -1 n z n 4 -1 -1 Pochhammer 1 -1 ν n -2 n -2 1 -1 ν -1 2 z -1 n -3 HypergeometricPFQ 3 4 -1 n 4 -1 1 -1 n 4 -1 5 4 -1 n 4 -1 3 2 -1 n 4 -1 3 2 1 -1 n 2 -1 3 2 -1 n 2 -1 1 -1 ν 2 -1 3 2 -1 ν 2 -1 -1 n 2 -1 ν 2 -1 1 -1 n 2 -1 ν 2 -1 3 2 -1 z 4 16 -1 KelvinBer -1 n ν -1 z 1 4 n 1 -1 KelvinBei -1 n ν -1 z 1 4 n 1 n n 3 [/itex]

 Rule Form

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 Contributed by

 Brychkov Yu.A. (2005)

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

 2007-05-02

© 1998-2013 Wolfram Research, Inc.