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 KelvinKer

 http://functions.wolfram.com/03.20.06.0008.01

 Input Form

 KelvinKer[\[Nu], z] == Sum[(1/(Subscript[z, 0]^k k!)) Sum[(-1)^(m + k) Binomial[k, m] Pochhammer[-\[Nu], k - m] Sum[(((-1)^i 2^(2 i - m) Pochhammer[-m, 2 (m - i)] Pochhammer[\[Nu], i])/(m - i)!) (KelvinKer[\[Nu], z] Sum[(((-1)^j (i - 2 j)!)/((2 j)! (i - 4 j)! Pochhammer[1 - i - \[Nu], 2 j] Pochhammer[\[Nu], 2 j])) (z/2)^(4 j), {j, 0, Floor[i/2]}] + (z/(2 Sqrt[2])) (KelvinKei[-1 + \[Nu], z] + KelvinKer[-1 + \[Nu], z]) Sum[(((-1)^j (i - 2 j - 1)!)/ ((2 j)! (i - 4 j - 1)! Pochhammer[1 - i - \[Nu], 2 j] Pochhammer[\[Nu], 2 j + 1])) (z/2)^(4 j), {j, 0, Floor[(i - 1)/2]}] + (z^2/4) KelvinKei[\[Nu], z] Sum[(((-1)^j (i - 2 j - 1)!)/((2 j + 1)! (i - 4 j - 2)! Pochhammer[1 - i - \[Nu], 2 j + 1] Pochhammer[\[Nu], 2 j + 1])) (z/2)^(4 j), {j, 0, Floor[(i - 1)/2]}] + (z^3/(8 Sqrt[2])) (KelvinKei[-1 + \[Nu], z] - KelvinKer[-1 + \[Nu], z]) Sum[(((-1)^j (i - 2 j - 2)!)/((2 j + 1)! (i - 4 j - 3)! Pochhammer[1 - i - \[Nu], 2 j + 1] Pochhammer[\[Nu], 2 j + 2])) (z/2)^(4 j), {j, 0, Floor[(i - 2)/2]}]) (z - Subscript[z, 0])^k, {i, 0, m}], {m, 0, k}], {k, 0, Infinity}] /; Abs[Arg[Subscript[z, 0]]] < Pi

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], RowBox[List[FractionBox[SubsuperscriptBox["z", "0", RowBox[List["-", "k"]]], RowBox[List["k", "!"]]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "0"]], "k"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["m", "+", "k"]]], RowBox[List["Binomial", "[", RowBox[List["k", ",", "m"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List["k", "-", "m"]]]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "m"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "i"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["2", " ", "i"]], "-", "m"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "m"]], ",", RowBox[List["2", " ", RowBox[List["(", RowBox[List["m", "-", "i"]], ")"]]]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", "i"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["m", "-", "i"]], ")"]], "!"]]], RowBox[List["(", " ", RowBox[List[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["Floor", "[", FractionBox["i", "2"], "]"]]], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["2", "j"]]]], ")"]], "!"]], " "]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["4", " ", "j"]]]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "i", "-", "\[Nu]"]], ",", RowBox[List["2", "j"]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", RowBox[List["2", "j"]]]], "]"]]]]], SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["4", "j"]]]]]]]]], "+", RowBox[List[FractionBox["z", RowBox[List["2", " ", SqrtBox["2"]]]], RowBox[List["(", RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", "z"]], "]"]], "+", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], ")"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["i", "-", "1"]], "2"], "]"]]], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["2", "j"]], "-", "1"]], ")"]], "!"]]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["4", " ", "j"]], "-", "1"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "i", "-", "\[Nu]"]], ",", RowBox[List["2", "j"]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", RowBox[List[RowBox[List["2", "j"]], "+", "1"]]]], "]"]]]]], " ", SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["4", "j"]]]]]]]]], "+", RowBox[List[FractionBox[SuperscriptBox["z", "2"], "4"], RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["i", "-", "1"]], "2"], "]"]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["2", "j"]], "-", "1"]], ")"]], "!"]]]], " ", ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "j"]], "+", "1"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["4", " ", "j"]], "-", "2"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "i", "-", "\[Nu]"]], ",", RowBox[List[RowBox[List["2", "j"]], "+", "1"]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", RowBox[List[RowBox[List["2", "j"]], "+", "1"]]]], "]"]]]], ")"]]]], SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["4", "j"]]]]]]]]], "+", RowBox[List[FractionBox[SuperscriptBox["z", "3"], RowBox[List["8", " ", SqrtBox["2"]]]], RowBox[List["(", RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", "z"]], "]"]], "-", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], ")"]], RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["i", "-", "2"]], "2"], "]"]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["2", "j"]], "-", "2"]], ")"]], "!"]]]], ")"]], "/", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", "j"]], "+", "1"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["4", " ", "j"]], "-", "3"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "i", "-", "\[Nu]"]], ",", RowBox[List[RowBox[List["2", "j"]], "+", "1"]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", RowBox[List[RowBox[List["2", "j"]], "+", "2"]]]], "]"]]]], ")"]]]], " ", SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["4", "j"]]]]]]]]]]], ")"]], SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["z", "0"]]], ")"]], "k"]]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", SubscriptBox["z", "0"], "]"]], "]"]], "<", "\[Pi]"]]]]]]

 MathML Form

 ker ν ( z ) k = 0 z 0 - k k ! m = 0 k ( - 1 ) k + m ( k m ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["k", Identity, Rule[Editable, True], Rule[Selectable, True]]], List[TagBox["m", Identity, Rule[Editable, True], Rule[Selectable, True]]]]], ")"]], InterpretTemplate[Function[Binomial[Slot[1], Slot[2]]]], Rule[Editable, False], Rule[Selectable, False]] ( - ν ) k - m TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", "\[Nu]"]], ")"]], RowBox[List["k", "-", "m"]]], Pochhammer] i = 0 m ( - 1 ) i 2 2 i - m ( - m ) 2 ( m - i ) TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", "m"]], ")"]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["m", "-", "i"]], ")"]]]]], Pochhammer] ( ν ) i TagBox[SubscriptBox[RowBox[List["(", "\[Nu]", ")"]], "i"], Pochhammer] ( m - i ) ! ( 1 4 z 2 kei ν ( z ) j = 0 i - 1 2 ( ( - 1 ) j ( i - 2 j - 1 ) ! ) ( z 2 ) 4 j ( 2 j + 1 ) ! ( i - 4 j - 2 ) ! ( - i - ν + 1 ) 2 j + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "i"]], "-", "\[Nu]", "+", "1"]], ")"]], RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]], Pochhammer] ( ν ) 2 j + 1 TagBox[SubscriptBox[RowBox[List["(", "\[Nu]", ")"]], RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]], Pochhammer] + z ( kei ν - 1 ( z ) + ker ν - 1 ( z ) ) 2 2 j = 0 i - 1 2 ( ( - 1 ) j ( i - 2 j - 1 ) ! ) ( z 2 ) 4 j ( 2 j ) ! ( i - 4 j - 1 ) ! ( - i - ν + 1 ) 2 j TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "i"]], "-", "\[Nu]", "+", "1"]], ")"]], RowBox[List["2", " ", "j"]]], Pochhammer] ( ν ) 2 j + 1 TagBox[SubscriptBox[RowBox[List["(", "\[Nu]", ")"]], RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]], Pochhammer] + z 3 ( kei ν - 1 ( z ) - ker ν - 1 ( z ) ) 8 2 j = 0 i - 2 2 ( ( - 1 ) j ( i - 2 j - 2 ) ! ) ( z 2 ) 4 j ( 2 j + 1 ) ! ( i - 4 j - 3 ) ! ( - i - ν + 1 ) 2 j + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "i"]], "-", "\[Nu]", "+", "1"]], ")"]], RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]], Pochhammer] ( ν ) 2 j + 2 TagBox[SubscriptBox[RowBox[List["(", "\[Nu]", ")"]], RowBox[List[RowBox[List["2", " ", "j"]], "+", "2"]]], Pochhammer] + ker ν ( z ) j = 0 i 2 ( ( - 1 ) j ( i - 2 j ) ! ) ( z 2 ) 4 j ( 2 j ) ! ( i - 4 j ) ! ( - i - ν + 1 ) 2 j TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "i"]], "-", "\[Nu]", "+", "1"]], ")"]], RowBox[List["2", " ", "j"]]], Pochhammer] ( ν ) 2 j TagBox[SubscriptBox[RowBox[List["(", "\[Nu]", ")"]], RowBox[List["2", " ", "j"]]], Pochhammer] ) ( z - z 0 ) k /; "\[LeftBracketingBar]" arg ( z 0 ) "\[RightBracketingBar]" < π Condition KelvinKer ν z k 0 Subscript z 0 -1 k k -1 m 0 k -1 k m Binomial k m Pochhammer -1 ν k -1 m i 0 m -1 i 2 2 i -1 m Pochhammer -1 m 2 m -1 i Pochhammer ν i m -1 i -1 1 4 z 2 KelvinKei ν z j 0 i -1 2 -1 -1 j i -1 2 j -1 z 2 -1 4 j 2 j 1 i -1 4 j -2 Pochhammer -1 i -1 ν 1 2 j 1 Pochhammer ν 2 j 1 -1 z KelvinKei ν -1 z KelvinKer ν -1 z 2 2 1 2 -1 j 0 i -1 2 -1 -1 j i -1 2 j -1 z 2 -1 4 j 2 j i -1 4 j -1 Pochhammer -1 i -1 ν 1 2 j Pochhammer ν 2 j 1 -1 z 3 KelvinKei ν -1 z -1 KelvinKer ν -1 z 8 2 1 2 -1 j 0 i -2 2 -1 -1 j i -1 2 j -2 z 2 -1 4 j 2 j 1 i -1 4 j -3 Pochhammer -1 i -1 ν 1 2 j 1 Pochhammer ν 2 j 2 -1 KelvinKer ν z j 0 i 2 -1 -1 j i -1 2 j z 2 -1 4 j 2 j i -1 4 j Pochhammer -1 i -1 ν 1 2 j Pochhammer ν 2 j -1 z -1 Subscript z 0 k Subscript z 0 [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "\[Infinity]"], FractionBox[RowBox[List[SubsuperscriptBox["zz", "0", RowBox[List["-", "k"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "0"]], "k"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["m", "+", "k"]]], " ", RowBox[List["Binomial", "[", RowBox[List["k", ",", "m"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List["k", "-", "m"]]]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["i", "=", "0"]], "m"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "i"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["2", " ", "i"]], "-", "m"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "m"]], ",", RowBox[List["2", " ", RowBox[List["(", RowBox[List["m", "-", "i"]], ")"]]]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", "i"]], "]"]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["Floor", "[", FractionBox["i", "2"], "]"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["2", " ", "j"]]]], ")"]], "!"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["4", " ", "j"]]]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", " ", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["4", " ", "j"]]]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "i", "-", "\[Nu]"]], ",", RowBox[List["2", " ", "j"]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", RowBox[List["2", " ", "j"]]]], "]"]]]]]]]]], "+", FractionBox[RowBox[List["z", " ", RowBox[List["(", RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", "z"]], "]"]], "+", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["i", "-", "1"]], "2"], "]"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["2", " ", "j"]], "-", "1"]], ")"]], "!"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["4", " ", "j"]]]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", " ", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["4", " ", "j"]], "-", "1"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "i", "-", "\[Nu]"]], ",", RowBox[List["2", " ", "j"]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]]], "]"]]]]]]]]], RowBox[List["2", " ", SqrtBox["2"]]]], "+", RowBox[List[FractionBox["1", "4"], " ", SuperscriptBox["z", "2"], " ", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["i", "-", "1"]], "2"], "]"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["2", " ", "j"]], "-", "1"]], ")"]], "!"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["4", " ", "j"]]]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["4", " ", "j"]], "-", "2"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "i", "-", "\[Nu]"]], ",", RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]]], "]"]]]]]]]]], "+", FractionBox[RowBox[List[SuperscriptBox["z", "3"], " ", RowBox[List["(", RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", "z"]], "]"]], "-", RowBox[List["KelvinKer", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "\[Nu]"]], ",", "z"]], "]"]]]], ")"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["j", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["i", "-", "2"]], "2"], "]"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["2", " ", "j"]], "-", "2"]], ")"]], "!"]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", FractionBox["z", "2"], ")"]], RowBox[List["4", " ", "j"]]]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["i", "-", RowBox[List["4", " ", "j"]], "-", "3"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "i", "-", "\[Nu]"]], ",", RowBox[List[RowBox[List["2", " ", "j"]], "+", "1"]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", RowBox[List[RowBox[List["2", " ", "j"]], "+", "2"]]]], "]"]]]]]]]]], RowBox[List["8", " ", SqrtBox["2"]]]]]], ")"]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["z", "-", SubscriptBox["zz", "0"]]], ")"]], "k"]]], RowBox[List[RowBox[List["(", RowBox[List["m", "-", "i"]], ")"]], "!"]]]]]]]]]]], RowBox[List["k", "!"]]]]], "/;", RowBox[List[RowBox[List["Abs", "[", RowBox[List["Arg", "[", SubscriptBox["zz", "0"], "]"]], "]"]], "<", "\[Pi]"]]]]]]]]

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

 2007-05-02