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variants of this functions
Hypergeometric1F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric1F1[a,b,z] > Specific values > Specialized values > For fixed a,z





http://functions.wolfram.com/07.20.03.0114.01









  


  










Input Form





Hypergeometric1F1[a, 2 a + n, z] == Gamma[a + 1/2] (z/4)^(-a + 1/2) E^(z/2) BesselI[a - 1/2, z/2] Sum[((-1)^(k - j) 2^(2 k - 4 j) z^(2 j - k) (k - j)! Pochhammer[1/2 + a, k] Pochhammer[2 a - 1, k] Pochhammer[-n, k])/(j! k! (k - 2 j)! Pochhammer[2 a + n, k] Pochhammer[3/2 - a - k, j] Pochhammer[a - 1/2, j]), {k, 0, n}, {j, 0, Floor[k/2]}] - Gamma[-(1/2) + a] E^(z/2) (z/4)^(-a + 3/2) BesselI[a - 3/2, z/2] Sum[((-1)^(k - j) 2^(2 k - 4 j) z^(2 j - k) (k - j - 1)! Pochhammer[1/2 + a, k] Pochhammer[-1 + 2 a, k] Pochhammer[-n, k])/(j! k! (k - 2 j - 1)! Pochhammer[2 a + n, k] Pochhammer[3/2 - a - k, j] Pochhammer[1/2 + a, j]), {k, 0, n}, {j, 0, Floor[(k - 1)/2]}] /; 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