Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3784)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=1, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=1, b₁=3

http://functions.wolfram.com/07.25.03.3784.01

Input Form

HypergeometricPFQ[{-(9/2), 1}, {3, 9/2}, z] == (14 (-5 + 13 z))/(143 z^2) + (1/(14057472 z^3)) (E^z (-135135 + 4809210 z - 8232084 z^2 + 4552920 z^3 - 1093840 z^4 + 124896 z^5 - 6592 z^6 + 128 z^7)) + (1/(28114944 z^(7/2))) (Sqrt[Pi] (135135 + 2162160 z - 15135120 z^2 + 20180160 z^3 - 10090080 z^4 + 2306304 z^5 - 256256 z^6 + 13312 z^7 - 256 z^8) Erfi[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},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁},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]