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; }

 KelvinBer

 http://functions.wolfram.com/03.14.06.0037.01

 Input Form

 KelvinBer[z] \[Proportional] ((1 + I)/(4 Sqrt[Pi])) (((E^((-1)^(3/4) z) - ((-1)^(1/4) z)/(E^((-1)^(3/4) z) Sqrt[(-I) z^2]))/ Sqrt[(-(-1)^(1/4)) z]) (Sum[(Pochhammer[1/2, 2 k]^2/(2 k)!) (I/(4 z^2))^k, {k, 0, Floor[n/2]}] + O[1/z^(2 Floor[n/2] + 2)]) + ((E^((-1)^(1/4) z) + ((-1)^(3/4) z)/(E^((-1)^(1/4) z) Sqrt[I z^2]))/ Sqrt[(-1)^(3/4) z]) (Sum[(Pochhammer[1/2, 2 k]^2/(2 k)!) (-(I/(4 z^2)))^k, {k, 0, Floor[n/2]}] + O[1/z^(2 Floor[n/2] + 2)]) + ((-1)^(3/4)/(2 z)) (((I E^((-1)^(3/4) z) - ((-1)^(1/4) Sqrt[(-I) z^2])/ (E^((-1)^(3/4) z) z))/Sqrt[(-(-1)^(1/4)) z]) (Sum[(Pochhammer[1/2, 1 + 2 k]^2/(1 + 2 k)!) (I/(4 z^2))^k, {k, 0, Floor[(n - 1)/2]}] + O[1/z^(2 Floor[(n - 1)/2] + 2)]) + ((-E^((-1)^(1/4) z) + ((-1)^(3/4) z)/(E^((-1)^(1/4) z) Sqrt[I z^2]))/ Sqrt[(-1)^(3/4) z]) (Sum[(Pochhammer[1/2, 1 + 2 k]^2/(1 + 2 k)!) (-(I/(4 z^2)))^k, {k, 0, Floor[(n - 1)/2]}] + O[1/z^(2 Floor[(n - 1)/2] + 2)]))) /; (Abs[z] -> Infinity) && Element[n, Integers] && n >= 0

 Standard Form

 Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["KelvinBer", "[", "z", "]"]], "\[Proportional]", RowBox[List[FractionBox[RowBox[List["1", "+", "\[ImaginaryI]"]], RowBox[List["4", SqrtBox["\[Pi]"]]]], " ", RowBox[List["(", RowBox[List[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", "z"]]], " ", "z"]], SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]]], RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]], RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["2", " ", "k"]]]], "]"]], "2"], RowBox[List[RowBox[List["(", RowBox[List["2", " ", "k"]], ")"]], "!"]]], SuperscriptBox[RowBox[List["(", FractionBox["\[ImaginaryI]", RowBox[List["4", SuperscriptBox["z", "2"]]]], ")"]], "k"]]]]], " ", "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", RowBox[List[RowBox[List["2", RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]]], "+", "2"]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]], "+", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", "z"]], SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]], ")"]], SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]]], RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]], RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["2", " ", "k"]]]], "]"]], "2"], RowBox[List[RowBox[List["(", RowBox[List["2", " ", "k"]], ")"]], "!"]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["\[ImaginaryI]", RowBox[List["4", SuperscriptBox["z", "2"]]]]]], ")"]], "k"]]]]], " ", "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", RowBox[List[RowBox[List["2", RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]]], "+", "2"]]]], "]"]]]], ")"]]]], " ", "+", RowBox[List[FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " "]], RowBox[List["2", " ", "z"]]], RowBox[List["(", RowBox[List[RowBox[List[FractionBox[RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]]]], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]], "z"]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]]], RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]], RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]]]], "]"]], "2"], RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]], ")"]], "!"]]], SuperscriptBox[RowBox[List["(", FractionBox["\[ImaginaryI]", RowBox[List["4", SuperscriptBox["z", "2"]]]], ")"]], "k"]]]]], " ", "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", RowBox[List[RowBox[List["2", RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]]], "+", "2"]]]], "]"]]]], ")"]]]], "+", RowBox[List[FractionBox[RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", "z"]], SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]], SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]]], RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]], RowBox[List[FractionBox[SuperscriptBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]]]], "]"]], "2"], RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]], ")"]], "!"]]], SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["\[ImaginaryI]", RowBox[List["4", SuperscriptBox["z", "2"]]]]]], ")"]], "k"]]]]], " ", "+", RowBox[List["O", "[", FractionBox["1", SuperscriptBox["z", RowBox[List[RowBox[List["2", RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]]], "+", "2"]]]], "]"]]]], ")"]]]]]], ")"]]]]]], ")"]]]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "\[And]", RowBox[List["n", "\[Element]", "Integers"]], "\[And]", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]

 MathML Form

 ber ( z ) 1 + 4 π ( 1 - - 1 4 z ( ( - 1 ) 3 / 4 z - - 1 4 - ( - 1 ) 3 / 4 z z - z 2 ) ( k = 0 n 2 ( 1 2 ) 2 k TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] 2 ( 2 k ) ! ( 4 z 2 ) k + O ( 1 z 2 n 2 + 2 ) ) + 1 ( - 1 ) 3 / 4 z ( ( - 1 ) 3 / 4 - - 1 4 z z z 2 + - 1 4 z ) ( k = 0 n 2 ( 1 2 ) 2 k TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] 2 ( 2 k ) ! ( - 4 z 2 ) k + O ( 1 z 2 n 2 + 2 ) ) + ( - 1 ) 3 / 4 2 z ( 1 - - 1 4 z ( ( - 1 ) 3 / 4 z - - 1 4 - ( - 1 ) 3 / 4 z - z 2 z ) ( k = 0 n - 1 2 ( 1 2 ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] 2 ( 2 k + 1 ) ! ( 4 z 2 ) k + O ( 1 z 2 n - 1 2 + 2 ) ) + 1 ( - 1 ) 3 / 4 z ( ( - 1 ) 3 / 4 - - 1 4 z z z 2 - - 1 4 z ) ( k = 0 n - 1 2 ( 1 2 ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", FractionBox["1", "2"], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] 2 ( 2 k + 1 ) ! ( - 4 z 2 ) k + O ( 1 z 2 n - 1 2 + 2 ) ) ) ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) n Condition Proportional KelvinBer z 1 4 1 2 -1 1 -1 -1 1 4 z 1 2 -1 -1 3 4 z -1 -1 1 4 -1 -1 3 4 z z -1 z 2 1 2 -1 k 0 n 2 -1 Pochhammer 1 2 2 k 2 2 k -1 4 z 2 -1 k O 1 z 2 n 2 -1 2 -1 1 -1 3 4 z 1 2 -1 -1 3 4 -1 -1 1 4 z z z 2 1 2 -1 -1 1 4 z k 0 n 2 -1 Pochhammer 1 2 2 k 2 2 k -1 -1 4 z 2 -1 k O 1 z 2 n 2 -1 2 -1 -1 3 4 2 z -1 1 -1 -1 1 4 z 1 2 -1 -1 3 4 z -1 -1 1 4 -1 -1 3 4 z -1 z 2 1 2 z -1 k 0 n -1 2 -1 Pochhammer 1 2 2 k 1 2 2 k 1 -1 4 z 2 -1 k O 1 z 2 n -1 2 -1 2 -1 1 -1 3 4 z 1 2 -1 -1 3 4 -1 -1 1 4 z z z 2 1 2 -1 -1 -1 1 4 z k 0 n -1 2 -1 Pochhammer 1 2 2 k 1 2 2 k 1 -1 -1 4 z 2 -1 k O 1 z 2 n -1 2 -1 2 -1 Rule z n [/itex]

 Rule Form

 Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinBer", "[", "z_", "]"]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["1", "+", "\[ImaginaryI]"]], ")"]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", "z"]]], " ", "z"]], SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["2", " ", "k"]]]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["(", FractionBox["\[ImaginaryI]", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]], ")"]], "k"]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", "k"]], ")"]], "!"]]]]], "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", RowBox[List[RowBox[List["2", " ", RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]]], "+", "2"]]]], "]"]]]], ")"]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]], "+", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", "z"]], SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["2", " ", "k"]]]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["\[ImaginaryI]", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]]]], ")"]], "k"]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", "k"]], ")"]], "!"]]]]], "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", RowBox[List[RowBox[List["2", " ", RowBox[List["Floor", "[", FractionBox["n", "2"], "]"]]]], "+", "2"]]]], "]"]]]], ")"]]]], SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]]], "+", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]]]], "-", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]]]], " ", "z"]]], " ", SqrtBox[RowBox[List[RowBox[List["-", "\[ImaginaryI]"]], " ", SuperscriptBox["z", "2"]]]]]], "z"]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]]]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["(", FractionBox["\[ImaginaryI]", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]], ")"]], "k"]]], RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]], ")"]], "!"]]]]], "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", RowBox[List[RowBox[List["2", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]]], "+", "2"]]]], "]"]]]], ")"]]]], SqrtBox[RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]]], "+", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["-", SuperscriptBox["\[ExponentialE]", RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]], " ", "z"]]]]], "+", FractionBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", SuperscriptBox["\[ExponentialE]", RowBox[List[RowBox[List["-", SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["1", "/", "4"]]]]], " ", "z"]]], " ", "z"]], SqrtBox[RowBox[List["\[ImaginaryI]", " ", SuperscriptBox["z", "2"]]]]]]], ")"]], " ", RowBox[List["(", RowBox[List[RowBox[List[UnderoverscriptBox["\[Sum]", RowBox[List["k", "=", "0"]], RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]], FractionBox[RowBox[List[SuperscriptBox[RowBox[List["Pochhammer", "[", RowBox[List[FractionBox["1", "2"], ",", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]]]], "]"]], "2"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["-", FractionBox["\[ImaginaryI]", RowBox[List["4", " ", SuperscriptBox["z", "2"]]]]]], ")"]], "k"]]], RowBox[List[RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "k"]]]], ")"]], "!"]]]]], "+", RowBox[List["SeriesData", "[", RowBox[List["z", ",", "\[Infinity]", ",", RowBox[List["{", "0", "}"]], ",", "0", ",", RowBox[List[RowBox[List["2", " ", RowBox[List["Floor", "[", FractionBox[RowBox[List["n", "-", "1"]], "2"], "]"]]]], "+", "2"]]]], "]"]]]], ")"]]]], SqrtBox[RowBox[List[SuperscriptBox[RowBox[List["(", RowBox[List["-", "1"]], ")"]], RowBox[List["3", "/", "4"]]], " ", "z"]]]]]], ")"]]]], RowBox[List["2", " ", "z"]]]]], ")"]]]], RowBox[List["4", " ", SqrtBox["\[Pi]"]]]], "/;", RowBox[List[RowBox[List["(", RowBox[List[RowBox[List["Abs", "[", "z", "]"]], "\[Rule]", "\[Infinity]"]], ")"]], "&&", RowBox[List["n", "\[Element]", "Integers"]], "&&", RowBox[List["n", "\[GreaterEqual]", "0"]]]]]]]]]]

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

 2007-05-02