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variants of this functions
LegendreQ




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LegendreQ[nu,mu,3,z] > Series representations > Generalized power series > Expansions at z==1





http://functions.wolfram.com/07.12.06.0010.01









  


  








Input Form





LegendreQ[n, m, 3, z] == (((-1)^(n - m - 1) (m + n)! (m - n - 1)!)/(2 m!)) ((z - 1)^(m/2)/(z + 1)^(m/2)) Sum[((Pochhammer[-n, k] Pochhammer[1 + n, k])/(Pochhammer[1 + m, k] k!)) ((1 - z)/2)^k, {k, 0, n}] + ((-1)^m/2) ((z + 1)^(m/2)/(z - 1)^(m/2)) Sum[(((m - k - 1)! Pochhammer[-n, k] Pochhammer[1 + n, k])/k!) ((z - 1)/2)^k, {k, 0, m - 1}] /; Abs[(1 - z)/2] < 1 && Element[n, Integers] && n >= 0 && Element[m, Integers] && m > 0 && m > n








Standard Form





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MathML Form







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Rule Form





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





2001-10-29