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StruveH






Mathematica Notation

Traditional Notation









Bessel-Type Functions > StruveH[nu,z] > Differentiation > Symbolic differentiation > With respect to z





http://functions.wolfram.com/03.09.20.0020.01









  


  










Input Form





D[StruveH[\[Nu], z], {z, n}] == (z^(1 - n + \[Nu])/(2^\[Nu] (Sqrt[Pi] Gamma[1/2 + \[Nu]]))) Sum[(-1)^(m + i) Binomial[i, m] Pochhammer[-\[Nu], i - m] Sum[(((-1)^(k - 1) 2^(2 k - m) Pochhammer[-m, 2 (m - k)] Pochhammer[\[Nu], k])/(m - k)!) Sum[((k - j - 1)! Pochhammer[2 j + \[Nu] - n + 2, n - i - 1] z^(2 j))/ (2^(2 j) (j! (k - 2 j - 1)! Pochhammer[1 - k - \[Nu], j] Pochhammer[\[Nu], j + 1])), {j, 0, k - 1}], {k, 0, m}], {i, 1, n - 1}, {m, 0, i}] + Sum[(-1)^(m + n) Binomial[n, m] Pochhammer[-\[Nu], n - m] Sum[(((-1)^(k - 1) 2^(2 k - m) Pochhammer[-m, 2 (m - k)] Pochhammer[\[Nu], k])/(m - k)!) ((z/2) Sum[((k - j - 1)!/(j! (k - 2 j - 1)! Pochhammer[1 - k - \[Nu], j] Pochhammer[\[Nu], j + 1])) (z^2/4)^j StruveH[\[Nu] - 1, z], {j, 0, k - 1}] - Sum[((k - j)!/(j! (k - 2 j)! Pochhammer[ 1 - k - \[Nu], j] Pochhammer[\[Nu], j])) (z^2/4)^j StruveH[\[Nu], z], {j, 0, k}]), {k, 0, m}], {m, 0, n}]/z^n /; Element[n, Integers] && n >= 0










Standard Form





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MathML Form







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





2007-05-02