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variants of this functions
Hypergeometric0F1




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric0F1[b,z] > Series representations > Asymptotic series expansions > Expansions for any z in exponential form





http://functions.wolfram.com/07.17.06.0008.01









  


  








Input Form





Hypergeometric0F1[b, z] \[Proportional] (Gamma[b]/(2 Sqrt[Pi])) (-z)^((1 - 2 b)/4) (E^(I (((1 - 2 b)/4) Pi + 2 Sqrt[-z])) (1 + (I (-3 + 2 b) (-1 + 2 b))/(16 Sqrt[-z]) + ((-5 + 2 b) (-3 + 2 b) (-1 + 2 b) (1 + 2 b))/(512 z) + \[Ellipsis]) + (1 - (I (-3 + 2 b) (-1 + 2 b))/(16 Sqrt[-z]) + ((-5 + 2 b) (-3 + 2 b) (-1 + 2 b) (1 + 2 b))/(512 z) + \[Ellipsis])/ E^(I (((1 - 2 b)/4) Pi + 2 Sqrt[-z]))) /; (Abs[z] -> Infinity)








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