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 KelvinKei

 http://functions.wolfram.com/03.19.06.0037.01

 Input Form

 KelvinKei[\[Nu], z] \[Proportional] ((Sqrt[Pi] Csc[Pi \[Nu]])/(4 Sqrt[2])) ((E^(z/Sqrt[2]) ((E^((I z)/Sqrt[2] - (5 I Pi \[Nu])/4) ((-1)^(3/4) z)^(-(1/2) + \[Nu]) (Sum[((Pochhammer[1/2 - \[Nu], 2 k] Pochhammer[1/2 + \[Nu], 2 k])/ (2^(2 k) (2 k)!)) (-(I/z^2))^k, {k, 0, Floor[n/2]}] + O[1/z^(2 Floor[n/2] + 2)]))/(-1)^4^(-1) + E^(-((I z)/Sqrt[2]) + (I Pi \[Nu])/4) ((-(-1)^(1/4)) z)^ (-(1/2) + \[Nu]) ((I Sqrt[(-I) z^2] Cos[Pi \[Nu]])/z - Sin[Pi \[Nu]]/(-1)^4^(-1)) (Sum[((Pochhammer[1/2 - \[Nu], 2 k] Pochhammer[1/2 + \[Nu], 2 k])/ (2^(2 k) (2 k)!)) (I/z^2)^k, {k, 0, Floor[n/2]}] + O[1/z^(2 Floor[n/2] + 2)])) + ((((-1)^(3/4) z)^(-(1/2) + \[Nu]) ((Sqrt[I z^2] Cos[Pi \[Nu]])/z + Sin[Pi \[Nu]]/(-1)^4^(-1)) (Sum[((Pochhammer[1/2 - \[Nu], 2 k] Pochhammer[1/2 + \[Nu], 2 k])/ (2^(2 k) (2 k)!)) (-(I/z^2))^k, {k, 0, Floor[n/2]}] + O[1/z^(2 Floor[n/2] + 2)]))/(E^((I z)/Sqrt[2]) E^((5 I Pi \[Nu])/4)) - (E^((I z)/Sqrt[2]) E^((I Pi \[Nu])/4) ((-(-1)^(1/4)) z)^(-(1/2) + \[Nu]) (Sum[((Pochhammer[1/2 - \[Nu], 2 k] Pochhammer[1/2 + \[Nu], 2 k])/ (2^(2 k) (2 k)!)) (I/z^2)^k, {k, 0, Floor[n/2]}] + O[1/z^(2 Floor[n/2] + 2)]))/(-1)^4^(-1))/E^(z/Sqrt[2]) + (I/(2 z)) (E^(z/Sqrt[2]) ((-E^((I z)/Sqrt[2] - (5 I Pi \[Nu])/4)) ((-1)^(3/4) z)^(-(1/2) + \[Nu]) (Sum[((Pochhammer[1/2 - \[Nu], 1 + 2 k] Pochhammer[1/2 + \[Nu], 1 + 2 k])/(2^(2 k) (1 + 2 k)!)) (-(I/z^2))^k, {k, 0, Floor[(n - 1)/2]}] + O[1/z^(2 Floor[(n - 1)/2] + 2)]) + E^(-((I z)/Sqrt[2]) + (I Pi \[Nu])/4) ((-(-1)^(1/4)) z)^ (-(1/2) + \[Nu]) (((-1)^(1/4) Sqrt[(-I) z^2] Cos[Pi \[Nu]])/z + I Sin[Pi \[Nu]]) (Sum[((Pochhammer[1/2 - \[Nu], 1 + 2 k] Pochhammer[1/2 + \[Nu], 1 + 2 k])/(2^(2 k) (1 + 2 k)!)) (I/z^2)^k, {k, 0, Floor[(n - 1)/2]}] + O[1/z^(2 Floor[(n - 1)/2] + 2)])) + (E^(-((I z)/Sqrt[2]) - (5 I Pi \[Nu])/4) ((-1)^(3/4) z)^ (-(1/2) + \[Nu]) (((-1)^(1/4) Sqrt[I z^2] Cos[Pi \[Nu]])/z + Sin[Pi \[Nu]]) (Sum[((Pochhammer[1/2 - \[Nu], 1 + 2 k] Pochhammer[1/2 + \[Nu], 1 + 2 k])/(2^(2 k) (1 + 2 k)!)) (-(I/z^2))^k, {k, 0, Floor[(n - 1)/2]}] + O[1/z^(2 Floor[(n - 1)/2] + 2)]) - I E^((I z)/Sqrt[2] + (I Pi \[Nu])/4) ((-(-1)^(1/4)) z)^ (-(1/2) + \[Nu]) (Sum[((Pochhammer[1/2 - \[Nu], 1 + 2 k] Pochhammer[1/2 + \[Nu], 1 + 2 k])/(2^(2 k) (1 + 2 k)!)) (I/z^2)^k, {k, 0, Floor[(n - 1)/2]}] + O[1/z^(2 Floor[(n - 1)/2] + 2)]))/E^(z/Sqrt[2])))/z^\[Nu] - z^\[Nu] ((E^(z/Sqrt[2]) ((E^((I z)/Sqrt[2] + (I Pi \[Nu])/4) ((-1)^(3/4) z)^(-(1/2) - \[Nu]) (Sum[((Pochhammer[1/2 - \[Nu], 2 k] Pochhammer[1/2 + \[Nu], 2 k])/( 2^(2 k) (2 k)!)) (-(I/z^2))^k, {k, 0, Floor[n/2]}] + O[1/z^(2 Floor[n/2] + 2)]))/(-1)^4^(-1) + E^(-((I z)/Sqrt[2]) + (3 I Pi \[Nu])/4) ((-(-1)^(1/4)) z)^ (-(1/2) - \[Nu]) (I Cos[Pi \[Nu]] (Sqrt[(-I) z^2]/z) + Sin[Pi \[Nu]]/(-1)^4^(-1)) (Sum[((Pochhammer[1/2 - \[Nu], 2 k] Pochhammer[1/2 + \[Nu], 2 k])/ (2^(2 k) (2 k)!)) (I/z^2)^k, {k, 0, Floor[n/2]}] + O[1/z^(2 Floor[n/2] + 2)])) + (E^(-((I z)/Sqrt[2]) + (I Pi \[Nu])/4) ((-1)^(3/4) z)^(-(1/2) - \[Nu]) (Cos[Pi \[Nu]] (Sqrt[I z^2]/z) - Sin[Pi \[Nu]]/(-1)^4^(-1)) (Sum[((Pochhammer[1/2 - \[Nu], 2 k] Pochhammer[1/2 + \[Nu], 2 k])/ (2^(2 k) (2 k)!)) (-(I/z^2))^k, {k, 0, Floor[n/2]}] + O[1/z^(2 Floor[n/2] + 2)]) - (E^((I z)/Sqrt[2] + (3 I Pi \[Nu])/4) ((-(-1)^(1/4)) z)^(-(1/2) - \[Nu]) (Sum[((Pochhammer[1/2 - \[Nu], 2 k] Pochhammer[1/2 + \[Nu], 2 k])/( 2^(2 k) (2 k)!)) (I/z^2)^k, {k, 0, Floor[n/2]}] + O[1/z^(2 Floor[n/2] + 2)]))/(-1)^4^(-1))/E^(z/Sqrt[2])) + (1/(2 z)) (E^(z/Sqrt[2]) ((-I) ((-1)^(3/4) z)^(-(1/2) - \[Nu]) E^((I z)/Sqrt[2] + (I Pi \[Nu])/4) (Sum[((Pochhammer[1/2 - \[Nu], 1 + 2 k] Pochhammer[1/2 + \[Nu], 1 + 2 k])/(2^(2 k) (1 + 2 k)!)) (-(I/z^2))^k, {k, 0, Floor[(n - 1)/2]}] + O[1/z^(2 Floor[(n - 1)/2] + 2)]) + ((-1)^(3/4) (Sqrt[(-I) z^2]/z) Cos[Pi \[Nu]] + Sin[Pi \[Nu]]) ((-(-1)^(1/4)) z)^(-(1/2) - \[Nu]) E^(-((I z)/Sqrt[2]) + (3 I Pi \[Nu])/4) (Sum[((Pochhammer[1/2 - \[Nu], 1 + 2 k] Pochhammer[1/2 + \[Nu], 1 + 2 k])/(2^(2 k) (1 + 2 k)!)) (I/z^2)^k, {k, 0, Floor[(n - 1)/2]}] + O[1/z^(2 Floor[(n - 1)/2] + 2)])) + (I ((-1)^(3/4) z)^(-(1/2) - \[Nu]) E^(-((I z)/Sqrt[2]) + (I Pi \[Nu])/4) ((-1)^(1/4) (Sqrt[I z^2]/z) Cos[Pi \[Nu]] - Sin[Pi \[Nu]]) (Sum[((Pochhammer[1/2 - \[Nu], 1 + 2 k] Pochhammer[1/2 + \[Nu], 1 + 2 k])/(2^(2 k) (1 + 2 k)!)) (-(I/z^2))^k, {k, 0, Floor[(n - 1)/2]}] + O[1/z^(2 Floor[(n - 1)/2] + 2)]) + E^((I z)/Sqrt[2] + (3 I Pi \[Nu])/4) ((-(-1)^(1/4)) z)^ (-(1/2) - \[Nu]) (Sum[((Pochhammer[1/2 - \[Nu], 1 + 2 k] Pochhammer[1/2 + \[Nu], 1 + 2 k])/(2^(2 k) (1 + 2 k)!)) (I/z^2)^k, {k, 0, Floor[(n - 1)/2]}] + O[1/z^(2 Floor[(n - 1)/2] + 2)]))/E^(z/Sqrt[2])))) /; (Abs[z] -> Infinity) && !Element[\[Nu], Integers] && Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 kei ν ( z ) π csc ( π ν ) 4 2 ( z - ν ( z 2 ( π ν 4 - z 2 ( - - 1 4 z ) ν - 1 2 ( - z 2 cos ( π ν ) z - 1 - 1 4 sin ( π ν ) ) ( k = 0 n 2 2 - 2 k ( 1 2 - ν ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( ν + 1 2 ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( 2 k ) ! ( z 2 ) k + O ( 1 z 2 n 2 + 2 ) ) + 1 - 1 4 z 2 - 5 π ν 4 ( ( - 1 ) 3 / 4 z ) ν - 1 2 ( k = 0 n 2 2 - 2 k ( 1 2 - ν ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( ν + 1 2 ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( 2 k ) ! ( - z 2 ) k + O ( 1 z 2 n 2 + 2 ) ) ) + - z 2 ( - z 2 - 1 4 ( 5 π ν ) ( ( - 1 ) 3 / 4 z ) ν - 1 2 ( z 2 cos ( π ν ) z + 1 - 1 4 sin ( π ν ) ) ( k = 0 n 2 2 - 2 k ( 1 2 - ν ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( ν + 1 2 ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( 2 k ) ! ( - z 2 ) k + O ( 1 z 2 n 2 + 2 ) ) - 1 - 1 4 z 2 π ν 4 ( - - 1 4 z ) ν - 1 2 ( k = 0 n 2 2 - 2 k ( 1 2 - ν ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( ν + 1 2 ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( 2 k ) ! ( z 2 ) k + O ( 1 z 2 n 2 + 2 ) ) ) + 2 z ( z 2 ( π ν 4 - z 2 ( - - 1 4 z ) ν - 1 2 ( - 1 4 - z 2 cos ( π ν ) z + sin ( π ν ) ) ( k = 0 n - 1 2 2 - 2 k ( 1 2 - ν ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( ν + 1 2 ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( 2 k + 1 ) ! ( z 2 ) k + O ( 1 z 2 n - 1 2 + 2 ) ) - z 2 - 5 π ν 4 ( ( - 1 ) 3 / 4 z ) ν - 1 2 ( k = 0 n - 1 2 2 - 2 k ( 1 2 - ν ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( ν + 1 2 ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( 2 k + 1 ) ! ( - z 2 ) k + O ( 1 z 2 n - 1 2 + 2 ) ) ) + - z 2 ( - z 2 - 5 π ν 4 ( ( - 1 ) 3 / 4 z ) ν - 1 2 ( - 1 4 z 2 cos ( π ν ) z + sin ( π ν ) ) ( k = 0 n - 1 2 2 - 2 k ( 1 2 - ν ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( ν + 1 2 ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( 2 k + 1 ) ! ( - z 2 ) k + O ( 1 z 2 n - 1 2 + 2 ) ) - z 2 + π ν 4 ( - - 1 4 z ) ν - 1 2 ( k = 0 n - 1 2 2 - 2 k ( 1 2 - ν ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( ν + 1 2 ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( 2 k + 1 ) ! ( z 2 ) k + O ( 1 z 2 n - 1 2 + 2 ) ) ) ) ) - z ν ( z 2 ( 3 π ν 4 - z 2 ( - - 1 4 z ) - ν - 1 2 ( - z 2 cos ( π ν ) z + 1 - 1 4 sin ( π ν ) ) ( k = 0 n 2 2 - 2 k ( 1 2 - ν ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( ν + 1 2 ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( 2 k ) ! ( z 2 ) k + O ( 1 z 2 n 2 + 2 ) ) + 1 - 1 4 z 2 + π ν 4 ( ( - 1 ) 3 / 4 z ) - ν - 1 2 ( k = 0 n 2 2 - 2 k ( 1 2 - ν ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( ν + 1 2 ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( 2 k ) ! ( - z 2 ) k + O ( 1 z 2 n 2 + 2 ) ) ) + - z 2 ( π ν 4 - z 2 ( ( - 1 ) 3 / 4 z ) - ν - 1 2 ( cos ( π ν ) z 2 z - 1 - 1 4 sin ( π ν ) ) ( k = 0 n 2 2 - 2 k ( 1 2 - ν ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( ν + 1 2 ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( 2 k ) ! ( - z 2 ) k + O ( 1 z 2 n 2 + 2 ) ) - 1 - 1 4 z 2 + 3 π ν 4 ( - - 1 4 z ) - ν - 1 2 ( k = 0 n 2 2 - 2 k ( 1 2 - ν ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( ν + 1 2 ) 2 k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List["2", " ", "k"]]], Pochhammer] ( 2 k ) ! ( z 2 ) k + O ( 1 z 2 n 2 + 2 ) ) ) + 1 2 z ( z 2 ( ( ( - 1 ) 3 / 4 - z 2 cos ( π ν ) z + sin ( π ν ) ) ( - - 1 4 z ) - ν - 1 2 3 π ν 4 - z 2 ( k = 0 n - 1 2 2 - 2 k ( 1 2 - ν ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( ν + 1 2 ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( 2 k + 1 ) ! ( z 2 ) k + O ( 1 z 2 n - 1 2 + 2 ) ) - ( ( - 1 ) 3 / 4 z ) - ν - 1 2 z 2 + π ν 4 ( k = 0 n - 1 2 2 - 2 k ( 1 2 - ν ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( ν + 1 2 ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( 2 k + 1 ) ! ( - z 2 ) k + O ( 1 z 2 n - 1 2 + 2 ) ) ) + - z 2 ( z 2 + 3 π ν 4 ( - - 1 4 z ) - ν - 1 2 ( k = 0 n - 1 2 2 - 2 k ( 1 2 - ν ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( ν + 1 2 ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( 2 k + 1 ) ! ( z 2 ) k + O ( 1 z 2 n - 1 2 + 2 ) ) + π ν 4 - z 2 ( ( - 1 ) 3 / 4 z ) - ν - 1 2 ( - 1 4 z 2 cos ( π ν ) z - sin ( π ν ) ) ( k = 0 n - 1 2 2 - 2 k ( 1 2 - ν ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["1", "2"], "-", "\[Nu]"]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( ν + 1 2 ) 2 k + 1 TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Nu]", "+", FractionBox["1", "2"]]], ")"]], RowBox[List[RowBox[List["2", " ", "k"]], "+", "1"]]], Pochhammer] ( 2 k + 1 ) ! ( - z 2 ) k + O ( 1 z 2 n - 1 2 + 2 ) ) ) ) ) ) /; ( "\[LeftBracketingBar]" z "\[RightBracketingBar]" "\[Rule]" ) ν TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] n TagBox["\[DoubleStruckCapitalN]", Function[List[], Integers]] Condition Proportional KelvinKei ν z 1 2 ν 4 2 1 2 -1 z -1 ν z 2 1 2 -1 ν 4 -1 -1 z 2 1 2 -1 -1 -1 1 4 z ν -1 1 2 -1 z 2 1 2 ν z -1 -1 1 -1 1 4 -1 ν k 0 n 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k Pochhammer ν 1 2 2 k 2 k -1 z 2 -1 k O 1 z 2 n 2 -1 2 -1 1 -1 1 4 -1 z 2 1 2 -1 -1 5 ν 4 -1 -1 3 4 z ν -1 1 2 k 0 n 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k Pochhammer ν 1 2 2 k 2 k -1 -1 z 2 -1 k O 1 z 2 n 2 -1 2 -1 -1 z 2 1 2 -1 -1 z 2 1 2 -1 -1 1 4 5 ν -1 3 4 z ν -1 1 2 z 2 1 2 ν z -1 1 -1 1 4 -1 ν k 0 n 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k Pochhammer ν 1 2 2 k 2 k -1 -1 z 2 -1 k O 1 z 2 n 2 -1 2 -1 -1 1 -1 1 4 -1 z 2 1 2 -1 ν 4 -1 -1 -1 1 4 z ν -1 1 2 k 0 n 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k Pochhammer ν 1 2 2 k 2 k -1 z 2 -1 k O 1 z 2 n 2 -1 2 -1 2 z -1 z 2 1 2 -1 ν 4 -1 -1 z 2 1 2 -1 -1 -1 1 4 z ν -1 1 2 -1 1 4 -1 z 2 1 2 ν z -1 ν k 0 n -1 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k 1 Pochhammer ν 1 2 2 k 1 2 k 1 -1 z 2 -1 k O 1 z 2 n -1 2 -1 2 -1 -1 z 2 1 2 -1 -1 5 ν 4 -1 -1 3 4 z ν -1 1 2 k 0 n -1 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k 1 Pochhammer ν 1 2 2 k 1 2 k 1 -1 -1 z 2 -1 k O 1 z 2 n -1 2 -1 2 -1 -1 z 2 1 2 -1 -1 z 2 1 2 -1 -1 5 ν 4 -1 -1 3 4 z ν -1 1 2 -1 1 4 z 2 1 2 ν z -1 ν k 0 n -1 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k 1 Pochhammer ν 1 2 2 k 1 2 k 1 -1 -1 z 2 -1 k O 1 z 2 n -1 2 -1 2 -1 -1 z 2 1 2 -1 ν 4 -1 -1 -1 1 4 z ν -1 1 2 k 0 n -1 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k 1 Pochhammer ν 1 2 2 k 1 2 k 1 -1 z 2 -1 k O 1 z 2 n -1 2 -1 2 -1 -1 z ν z 2 1 2 -1 3 ν 4 -1 -1 z 2 1 2 -1 -1 -1 1 4 z -1 ν -1 1 2 -1 z 2 1 2 ν z -1 1 -1 1 4 -1 ν k 0 n 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k Pochhammer ν 1 2 2 k 2 k -1 z 2 -1 k O 1 z 2 n 2 -1 2 -1 1 -1 1 4 -1 z 2 1 2 -1 ν 4 -1 -1 3 4 z -1 ν -1 1 2 k 0 n 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k Pochhammer ν 1 2 2 k 2 k -1 -1 z 2 -1 k O 1 z 2 n 2 -1 2 -1 -1 z 2 1 2 -1 ν 4 -1 -1 z 2 1 2 -1 -1 3 4 z -1 ν -1 1 2 ν z 2 1 2 z -1 -1 1 -1 1 4 -1 ν k 0 n 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k Pochhammer ν 1 2 2 k 2 k -1 -1 z 2 -1 k O 1 z 2 n 2 -1 2 -1 -1 1 -1 1 4 -1 z 2 1 2 -1 3 ν 4 -1 -1 -1 1 4 z -1 ν -1 1 2 k 0 n 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k Pochhammer ν 1 2 2 k 2 k -1 z 2 -1 k O 1 z 2 n 2 -1 2 -1 1 2 z -1 z 2 1 2 -1 -1 3 4 -1 z 2 1 2 ν z -1 ν -1 -1 1 4 z -1 ν -1 1 2 3 ν 4 -1 -1 z 2 1 2 -1 k 0 n -1 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k 1 Pochhammer ν 1 2 2 k 1 2 k 1 -1 z 2 -1 k O 1 z 2 n -1 2 -1 2 -1 -1 -1 3 4 z -1 ν -1 1 2 z 2 1 2 -1 ν 4 -1 k 0 n -1 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k 1 Pochhammer ν 1 2 2 k 1 2 k 1 -1 -1 z 2 -1 k O 1 z 2 n -1 2 -1 2 -1 -1 z 2 1 2 -1 z 2 1 2 -1 3 ν 4 -1 -1 -1 1 4 z -1 ν -1 1 2 k 0 n -1 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k 1 Pochhammer ν 1 2 2 k 1 2 k 1 -1 z 2 -1 k O 1 z 2 n -1 2 -1 2 -1 ν 4 -1 -1 z 2 1 2 -1 -1 3 4 z -1 ν -1 1 2 -1 1 4 z 2 1 2 ν z -1 -1 ν k 0 n -1 2 -1 2 -2 k Pochhammer 1 2 -1 ν 2 k 1 Pochhammer ν 1 2 2 k 1 2 k 1 -1 -1 z 2 -1 k O 1 z 2 n -1 2 -1 2 -1 Rule z ν n [/itex]

 Rule Form

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

 2007-05-02