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; }

 KelvinKer

 http://functions.wolfram.com/03.20.20.0013.01

 Input Form

 D[KelvinKer[\[Nu], z], {z, n}] == Sum[(-1)^(m + n) Binomial[n, m] Pochhammer[-\[Nu], n - m] Sum[(((-1)^k 2^(2 k - m) Pochhammer[-m, 2 (m - k)] Pochhammer[\[Nu], k])/ (m - k)!) (KelvinKer[\[Nu], z] Sum[(((-1)^j (k - 2 j)!)/ ((2 j)! (k - 4 j)! Pochhammer[1 - k - \[Nu], 2 j] Pochhammer[\[Nu], 2 j])) (z/2)^(4 j), {j, 0, Floor[k/2]}] + (z/(2 Sqrt[2])) (KelvinKei[-1 + \[Nu], z] + KelvinKer[-1 + \[Nu], z]) Sum[(((-1)^j (k - 2 j - 1)!)/((2 j)! (k - 4 j - 1)! Pochhammer[1 - k - \[Nu], 2 j] Pochhammer[\[Nu], 2 j + 1])) (z/2)^(4 j), {j, 0, Floor[(k - 1)/2]}] + (z^2/4) KelvinKei[\[Nu], z] Sum[(((-1)^j (k - 2 j - 1)!)/ ((2 j + 1)! (k - 4 j - 2)! Pochhammer[1 - k - \[Nu], 2 j + 1] Pochhammer[\[Nu], 2 j + 1])) (z/2)^(4 j), {j, 0, Floor[(k - 1)/2]}] + (z^3/(8 Sqrt[2])) (KelvinKei[-1 + \[Nu], z] - KelvinKer[-1 + \[Nu], z]) Sum[(((-1)^j (k - 2 j - 2)!)/((2 j + 1)! (k - 4 j - 3)! Pochhammer[1 - k - \[Nu], 2 j + 1] Pochhammer[\[Nu], 2 j + 2])) (z/2)^(4 j), {j, 0, Floor[(k - 2)/2]}]), {k, 0, m}], {m, 0, n}]/ z^n /; Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SubscriptBox["\[PartialD]", RowBox[List["{", RowBox[List["z", ",", "n"]], "}"]]], RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]]]], "\[Equal]", RowBox[List[SuperscriptBox["z", RowBox[List["-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "0"]], "n"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["m", "+", "n"]]], RowBox[List["Binomial", "[", RowBox[List["n", ",", "m"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List["n", "-", "m"]]]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "m"], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "m"]], ",", RowBox[List["2", " ", RowBox[List["(", RowBox[List["m", "-", "k"]], ")"]]]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", "k"]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["m", "-", "k"]], ")"]], "!"]]], 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["k", "2"], "]"]]], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], RowBox[List[RowBox[List["(", RowBox[List["k", "-", RowBox[List["2", "j"]]]], ")"]], "!"]], " "]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["k", "-", RowBox[List["4", " ", "j"]]]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "k", "-", "\[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["k", "-", "1"]], "2"], "]"]]], RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], RowBox[List[RowBox[List["(", RowBox[List["k", "-", RowBox[List["2", "j"]], "-", "1"]], ")"]], "!"]]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List["2", "j"]], ")"]], "!"]], " ", RowBox[List[RowBox[List["(", RowBox[List["k", "-", RowBox[List["4", " ", "j"]], "-", "1"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "k", "-", "\[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["k", "-", "1"]], "2"], "]"]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], RowBox[List[RowBox[List["(", RowBox[List["k", "-", 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["k", "-", RowBox[List["4", " ", "j"]], "-", "2"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "k", "-", "\[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["k", "-", "2"]], "2"], "]"]]], RowBox[List[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], RowBox[List[RowBox[List["(", RowBox[List["k", "-", 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["k", "-", RowBox[List["4", " ", "j"]], "-", "3"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "k", "-", "\[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"]]]]]]]]]]], ")"]]]]]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 n ker ν ( z ) z n z - n m = 0 n ( - 1 ) m + n ( n m ) TagBox[RowBox[List["(", GridBox[List[List[TagBox["n", 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 ) n - m TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", "\[Nu]"]], ")"]], RowBox[List["n", "-", "m"]]], Pochhammer] k = 0 m ( - 1 ) k 2 2 k - m ( - m ) 2 ( m - k ) TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", "m"]], ")"]], RowBox[List["2", " ", RowBox[List["(", RowBox[List["m", "-", "k"]], ")"]]]]], Pochhammer] ( ν ) k TagBox[SubscriptBox[RowBox[List["(", "\[Nu]", ")"]], "k"], Pochhammer] ( m - k ) ! ( ker ν ( z ) j = 0 k 2 ( - 1 ) j ( k - 2 j ) ! ( 2 j ) ! ( k - 4 j ) ! ( - k - ν + 1 ) 2 j TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "-", "\[Nu]", "+", "1"]], ")"]], RowBox[List["2", " ", "j"]]], Pochhammer] ( ν ) 2 j TagBox[SubscriptBox[RowBox[List["(", "\[Nu]", ")"]], RowBox[List["2", " ", "j"]]], Pochhammer] ( z 2 ) 4 j + z 2 2 ( kei ν - 1 ( z ) + ker ν - 1 ( z ) ) j = 0 k - 1 2 ( - 1 ) j ( - 2 j + k - 1 ) ! ( 2 j ) ! ( - 4 j + k - 1 ) ! ( - k - ν + 1 ) 2 j TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "-", "\[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 2 ) 4 j + z 2 4 kei ν ( z ) j = 0 k - 1 2 ( - 1 ) j ( - 2 j + k - 1 ) ! ( 2 j + 1 ) ! ( - 4 j + k - 2 ) ! ( - k - ν + 1 ) 2 j + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "-", "\[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 2 ) 4 j + z 3 8 2 ( kei ν - 1 ( z ) - ker ν - 1 ( z ) ) j = 0 k - 2 2 ( - 1 ) j ( - 2 j + k - 2 ) ! ( 2 j + 1 ) ! ( - 4 j + k - 3 ) ! ( - k - ν + 1 ) 2 j + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", "k"]], "-", "\[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] ( z 2 ) 4 j ) /; n Condition z n KelvinKer ν z z -1 n m 0 n -1 m n Binomial n m Pochhammer -1 ν n -1 m k 0 m -1 k 2 2 k -1 m Pochhammer -1 m 2 m -1 k Pochhammer ν k m -1 k -1 KelvinKer ν z j 0 k 2 -1 -1 j k -1 2 j 2 j k -1 4 j Pochhammer -1 k -1 ν 1 2 j Pochhammer ν 2 j -1 z 2 -1 4 j z 2 2 1 2 -1 KelvinKei ν -1 z KelvinKer ν -1 z j 0 k -1 2 -1 -1 j -2 j k -1 2 j -4 j k -1 Pochhammer -1 k -1 ν 1 2 j Pochhammer ν 2 j 1 -1 z 2 -1 4 j z 2 4 -1 KelvinKei ν z j 0 k -1 2 -1 -1 j -2 j k -1 2 j 1 -4 j k -2 Pochhammer -1 k -1 ν 1 2 j 1 Pochhammer ν 2 j 1 -1 z 2 -1 4 j z 3 8 2 1 2 -1 KelvinKei ν -1 z -1 KelvinKer ν -1 z j 0 k -2 2 -1 -1 j -2 j k -2 2 j 1 -4 j k -3 Pochhammer -1 k -1 ν 1 2 j 1 Pochhammer ν 2 j 2 -1 z 2 -1 4 j n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SubscriptBox["\[PartialD]", RowBox[List[RowBox[List["{", RowBox[List["z_", ",", "n_"]], "}"]]]]], RowBox[List["KelvinKer", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["z", RowBox[List["-", "n"]]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["m", "=", "0"]], "n"], RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["m", "+", "n"]]], " ", RowBox[List["Binomial", "[", RowBox[List["n", ",", "m"]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", RowBox[List["n", "-", "m"]]]], "]"]], " ", RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], "m"], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "k"], " ", SuperscriptBox["2", RowBox[List[RowBox[List["2", " ", "k"]], "-", "m"]]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["-", "m"]], ",", RowBox[List["2", " ", RowBox[List["(", RowBox[List["m", "-", "k"]], ")"]]]]]], "]"]], " ", RowBox[List["Pochhammer", "[", RowBox[List["\[Nu]", ",", "k"]], "]"]]]], ")"]], " ", 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["k", "2"], "]"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", RowBox[List[RowBox[List["(", RowBox[List["k", "-", 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["k", "-", RowBox[List["4", " ", "j"]]]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "k", "-", "\[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["k", "-", "1"]], "2"], "]"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", RowBox[List[RowBox[List["(", RowBox[List["k", "-", 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["k", "-", RowBox[List["4", " ", "j"]], "-", "1"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "k", "-", "\[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["k", "-", "1"]], "2"], "]"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", RowBox[List[RowBox[List["(", RowBox[List["k", "-", 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["k", "-", RowBox[List["4", " ", "j"]], "-", "2"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "k", "-", "\[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["k", "-", "2"]], "2"], "]"]]], FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], "j"], " ", RowBox[List[RowBox[List["(", RowBox[List["k", "-", 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["k", "-", RowBox[List["4", " ", "j"]], "-", "3"]], ")"]], "!"]], " ", RowBox[List["Pochhammer", "[", RowBox[List[RowBox[List["1", "-", "k", "-", "\[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"]]]]]], ")"]]]], RowBox[List[RowBox[List["(", RowBox[List["m", "-", "k"]], ")"]], "!"]]]]]]]]]]], "/;", RowBox[List[RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2007-05-02