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variants of this functions
HypergeometricPFQRegularized






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricPFQRegularized[{a1,...,ap},{b1,...,bq},z] > Series representations > Asymptotic series expansions > Expansions for 0F3





http://functions.wolfram.com/07.32.06.0036.01









  


  










Input Form





HypergeometricPFQRegularized[{}, {Subscript[b, 1], Subscript[b, 2], Subscript[b, 3]}, z] \[Proportional] (1/(4 Sqrt[2] Pi^(3/2))) E^(4 z^(1/4)) z^((1/4) (3/2 - Subscript[b, 1] - Subscript[b, 2] - Subscript[b, 3])) (1 + (-7 - 12 Subscript[b, 1]^2 - 12 Subscript[b, 2]^2 + 8 Subscript[b, 3] - 12 Subscript[b, 3]^2 + 8 Subscript[b, 2] (1 + Subscript[b, 3]) + 8 Subscript[b, 1] (1 + Subscript[b, 2] + Subscript[b, 3]))/(32 z^(1/4)) + (1/(2048 Sqrt[z])) (121 + 144 Subscript[b, 1]^4 + 144 Subscript[b, 2]^4 - 176 Subscript[b, 3] + 8 Subscript[b, 3]^2 - 64 Subscript[b, 3]^3 + 144 Subscript[b, 3]^4 - 64 Subscript[b, 2]^3 (1 + 3 Subscript[b, 3]) - 64 Subscript[b, 1]^3 (1 + 3 Subscript[b, 2] + 3 Subscript[b, 3]) + 8 Subscript[b, 2]^2 (1 - 24 Subscript[b, 3] + 44 Subscript[b, 3]^2) - 16 Subscript[b, 2] (11 - 21 Subscript[b, 3] + 12 Subscript[b, 3]^2 + 12 Subscript[b, 3]^3) + 8 Subscript[b, 1]^2 (1 + 44 Subscript[b, 2]^2 - 24 Subscript[b, 3] + 44 Subscript[b, 3]^2 - 8 Subscript[b, 2] (3 + Subscript[b, 3])) - 16 Subscript[b, 1] (11 + 12 Subscript[b, 2]^3 - 21 Subscript[b, 3] + 12 Subscript[b, 3]^2 + 12 Subscript[b, 3]^3 + 4 Subscript[b, 2]^2 (3 + Subscript[b, 3]) + Subscript[b, 2] (-21 - 40 Subscript[b, 3] + 4 Subscript[b, 3]^2))) + \[Ellipsis]) /; (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





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