Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am0c)

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.am0c.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(9/2), 11/2}, -z] == (1/(315 z^4)) (76204800 + 25401600 z + 7620480 z^2 + 1814400 z^3 + 353115 z^4 + 57960 z^5 + 8280 z^6 + 1104 z^7 + 210 z^8 + 294 z^9 - 104 z^10 + 8 z^11) + (1/(315 z^(9/2))) ((Sqrt[Pi] (-38102400 - 38102400 z - 19051200 z^2 - 6350400 z^3 - 1587600 z^4 - 317520 z^5 - 52920 z^6 - 7560 z^7 - 945 z^8 - 105 z^9 - 342 z^10 + 108 z^11 - 8 z^12) Erfi[Sqrt[z]])/E^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]
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