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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/07.20.03.0113.01









  


  










Input Form





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





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