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; }

 WhittakerM

 http://functions.wolfram.com/07.44.03.0017.01

 Input Form

 WhittakerM[-(n/2), \[Mu], z] == 2^(-2 + n + 2 \[Mu]) z^((1 - n)/2) (4 BesselI[n/2 + \[Mu], z/2] Gamma[1 + n/2 + \[Mu]] Sum[((-1)^(-j - k + n) z^(2 j - k + n) (-j + k)! Pochhammer[-n, -k + n] Pochhammer[-n + 2 \[Mu], -k + n])/2^(2 (2 j - k + n))/ (j! (-2 j + k)! (-k + n)! Pochhammer[-(n/2) - \[Mu], j] Pochhammer[-(n/2) + \[Mu], -k + n] Pochhammer[1 - k + n/2 + \[Mu], j] Pochhammer[1 + 2 \[Mu], -k + n]), {k, 0, n}, {j, 0, Floor[k/2]}] + z BesselI[1 + n/2 + \[Mu], z/2] Gamma[n/2 + \[Mu]] Sum[((-1)^(-j - k + n) z^(2 j - k + n) (-1 - j + k)! Pochhammer[-n, -k + n] Pochhammer[-n + 2 \[Mu], -k + n])/ 2^(2 (2 j - k + n))/(j! (-1 - 2 j + k)! (-k + n)! Pochhammer[1 - n/2 - \[Mu], j] Pochhammer[-(n/2) + \[Mu], -k + n] Pochhammer[1 - k + n/2 + \[Mu], j] Pochhammer[1 + 2 \[Mu], -k + n]), {k, 0, n}, {j, 0, Floor[(1/2) (-1 + k)]}]) /; Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 M TagBox["M", WhittakerM] - n 2 , μ ( z ) 2 n + 2 μ - 2 z 1 - n 2 ( 4 I n 2 + μ ( z 2 ) Γ ( n 2 + μ + 1 ) k = 0 n j = 0 k 2 ( - 1 ) n - j - k 2 - 2 ( 2 j - k + n ) ( k - j ) ! ( - n ) n - k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", "n"]], ")"]], RowBox[List["n", "-", "k"]]], Pochhammer] ( 2 μ - n ) n - k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "-", "n"]], ")"]], RowBox[List["n", "-", "k"]]], Pochhammer] z 2 j - k + n j ! ( k - 2 j ) ! ( n - k ) ! ( - n 2 - μ ) j TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["-", FractionBox["n", "2"]]], "-", "\[Mu]"]], ")"]], "j"], Pochhammer] ( μ - n 2 ) n - k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Mu]", "-", FractionBox["n", "2"]]], ")"]], RowBox[List["n", "-", "k"]]], Pochhammer] ( n 2 + μ - k + 1 ) j TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["n", "2"], "+", "\[Mu]", "-", "k", "+", "1"]], ")"]], "j"], Pochhammer] ( 2 μ + 1 ) n - k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "1"]], ")"]], RowBox[List["n", "-", "k"]]], Pochhammer] + z I n 2 + μ + 1 ( z 2 ) Γ ( n 2 + μ ) k = 0 n j = 0 k - 1 2 ( - 1 ) n - j - k 2 - 2 ( 2 j - k + n ) ( k - j - 1 ) ! ( - n ) n - k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["-", "n"]], ")"]], RowBox[List["n", "-", "k"]]], Pochhammer] ( 2 μ - n ) n - k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "-", "n"]], ")"]], RowBox[List["n", "-", "k"]]], Pochhammer] z 2 j - k + n j ! ( k - 2 j - 1 ) ! ( n - k ) ! ( 1 - n 2 - μ ) j TagBox[SubscriptBox[RowBox[List["(", RowBox[List["1", "-", FractionBox["n", "2"], "-", "\[Mu]"]], ")"]], "j"], Pochhammer] ( μ - n 2 ) n - k TagBox[SubscriptBox[RowBox[List["(", RowBox[List["\[Mu]", "-", FractionBox["n", "2"]]], ")"]], RowBox[List["n", "-", "k"]]], Pochhammer] ( n 2 + μ - k + 1 ) j TagBox[SubscriptBox[RowBox[List["(", RowBox[List[FractionBox["n", "2"], "+", "\[Mu]", "-", "k", "+", "1"]], ")"]], "j"], Pochhammer] ( 2 μ + 1 ) n - k TagBox[SubscriptBox[RowBox[List["(", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "+", "1"]], ")"]], RowBox[List["n", "-", "k"]]], Pochhammer] ) /; n Condition WhittakerM -1 n 2 -1 μ z 2 n 2 μ -2 z 1 -1 n 2 -1 4 BesselI n 2 -1 μ z 2 -1 Gamma n 2 -1 μ 1 j 0 k 2 -1 k 0 n -1 n -1 j -1 k 2 -2 2 j -1 k n k -1 j Pochhammer -1 n n -1 k Pochhammer 2 μ -1 n n -1 k z 2 j -1 k n j k -1 2 j n -1 k Pochhammer -1 n 2 -1 -1 μ j Pochhammer μ -1 n 2 -1 n -1 k Pochhammer n 2 -1 μ -1 k 1 j Pochhammer 2 μ 1 n -1 k -1 z BesselI n 2 -1 μ 1 z 2 -1 Gamma n 2 -1 μ j 0 k -1 2 -1 k 0 n -1 n -1 j -1 k 2 -2 2 j -1 k n k -1 j -1 Pochhammer -1 n n -1 k Pochhammer 2 μ -1 n n -1 k z 2 j -1 k n j k -1 2 j -1 n -1 k Pochhammer 1 -1 n 2 -1 -1 μ j Pochhammer μ -1 n 2 -1 n -1 k Pochhammer n 2 -1 μ -1 k 1 j Pochhammer 2 μ 1 n -1 k -1 n [/itex]

 Rule Form

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

 2007-05-02