Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ah0f)

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=5, b₁>=-11/2

For fixed z and a₁=3/2, a₂=5, b₁=-9/2

http://functions.wolfram.com/07.25.03.ah0f.01

Input Form

HypergeometricPFQ[{3/2, 5}, {-(9/2), 11/2}, z] == (1/(96 z^4)) (6350400 - 2419200 z + 758520 z^2 - 190800 z^3 + 39564 z^4 - 6960 z^5 + 1065 z^6 - 146 z^7 + 20 z^8 - 8 z^9) + (1/(192 z^(9/2))) (E^z Sqrt[Pi] (-6350400 + 6652800 z - 3500280 z^2 + 1234080 z^3 - 328140 z^4 + 70200 z^5 - 12585 z^6 + 1944 z^7 - 264 z^8 + 32 z^9 - 16 z^10) Erf[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]