Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9gk)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.a9gk.01

Input Form

HypergeometricPFQ[{-(9/4)}, {-(1/2), 19/4}, z] == -((1/(51539607552 z^(15/4))) ((77 (4 z^(1/4) (-310134825 - 413513100 Sqrt[z] - 171596880 z + 23250240 z^(3/2) + 15828480 z^2 - 26818560 z^(5/2) + 14376960 z^3 - 39419904 z^(7/2) + 9633792 z^4 - 41680896 z^(9/2) - 1048576 z^5 + 4194304 z^(11/2) + E^(4 Sqrt[z]) (310134825 - 413513100 Sqrt[z] + 171596880 z + 23250240 z^(3/2) - 15828480 z^2 - 26818560 z^(5/2) - 14376960 z^3 - 39419904 z^(7/2) - 9633792 z^4 - 41680896 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (310134825 - 159213600 z + 69984000 z^2 - 55296000 z^3 - 132710400 z^4 - 169869312 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (310134825 - 159213600 z + 69984000 z^2 - 55296000 z^3 - 132710400 z^4 - 169869312 z^5 + 16777216 z^6) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])))

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

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]