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BesselI






Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselI[nu,z] > Differentiation > Low-order differentiation > With respect to nu





http://functions.wolfram.com/03.02.20.0018.01









  


  










Input Form





Derivative[1, 0][BesselI][-n, z] == Sum[(((-1)^(n - k - 1) (n - k - 1)!)/k!) (z/2)^(2 k - n), {k, 0, n - 1}] - (-1)^n BesselK[n, z] + ((n!/2) Sum[((-1)^k/((n - k) k!)) BesselI[k, z] (z/2)^k, {k, 0, n - 1}])/ (-(z/2))^n + (1/n!) (z/2)^n Sum[(1/j) HypergeometricPFQ[{j}, {1 + j, 1 + n}, z^2/4], {j, 1, n}] /; Element[n, Integers] && n > 0










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)





2007-05-02





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