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 WhittakerW

 http://functions.wolfram.com/07.45.03.0032.01

 Input Form

 WhittakerW[m/2 - n, (m - 1)/2, z] == (m - 1) z^(m/2) E^(z/2) Sum[(((-1)^q z^(n - p - q - m) (m + k - 2)!)/(p! k! (n - m - p - q)! (n - p - 1)! (q - k)!)) (Sum[z^j/Pochhammer[q - k - m + 1, m - q + k + j], {j, 0, q - k - m}]/ E^z - Sum[z^j/Pochhammer[q - k - m + 1, m - q + k + j], {j, q - k - m + 1, -1}]/E^z + ((-1)^(m + q - k)/(m - q + k - 1)!) (ExpIntegralEi[-z] - (1/2) (Log[-z] - Log[-(1/z)]) + Log[z])), {p, 0, n - m}, {q, 0, n - m}, {k, 0, q}] /; Element[n, Integers] && n > 1 && Element[m, Integers] && Inequality[1, Less, m, LessEqual, n]

 Standard Form

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 MathML Form

 W TagBox["W", WhittakerW] m 2 - n , m - 1 2 ( z ) ( m - 1 ) z m / 2 z / 2 p = 0 n - m q = 0 n - m k = 0 q ( - 1 ) q z n - m - p - q ( k + m - 2 ) ! p ! k ! ( n - m - p - q ) ! ( n - p - 1 ) ! ( q - k ) ! ( ( - 1 ) q - k + m ( k + m - q - 1 ) ! ( Ei ( - z ) - 1 2 ( log ( - z ) - log ( - 1 z ) ) + log ( z ) ) + - z j = 0 q - k - m z j ( q - k - m + 1 ) j + k + m - q TagBox[SubscriptBox[RowBox[List["(", RowBox[List["q", "-", "k", "-", "m", "+", "1"]], ")"]], RowBox[List["j", "+", "k", "+", "m", "-", "q"]]], Pochhammer] - - z j = q - k - m + 1 - 1 z j ( q - k - m + 1 ) j + k + m - q TagBox[SubscriptBox[RowBox[List["(", RowBox[List["q", "-", "k", "-", "m", "+", "1"]], ")"]], RowBox[List["j", "+", "k", "+", "m", "-", "q"]]], Pochhammer] ) /; n TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] n > 1 m TagBox["\[DoubleStruckCapitalZ]", Function[Integers]] 1 < m n Condition WhittakerW m 2 -1 -1 n m -1 2 -1 z m -1 z m 2 -1 z 2 -1 k 0 q q 0 n -1 m p 0 n -1 m -1 q z n -1 m -1 p -1 q k m -2 p k n -1 m -1 p -1 q n -1 p -1 q -1 k -1 -1 q -1 k m k m -1 q -1 -1 ExpIntegralEi -1 z -1 1 2 -1 z -1 -1 1 z -1 z -1 z j 0 q -1 k -1 m z j Pochhammer q -1 k -1 m 1 j k m -1 q -1 -1 -1 z j q -1 k -1 m 1 -1 z j Pochhammer q -1 k -1 m 1 j k m -1 q -1 n n 1 m Inequality 1 m n [/itex]

 Rule Form

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

 2007-05-02