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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{4, 11/2}, {-(9/2), 6}, z] == (97240 (-76 + z))/(21 z^5) - (1/(178605 z^5)) (4 E^z (-15713497800 + 15920254350 z - 8063505450 z^2 + 2722294575 z^3 - 689188500 z^4 + 139516020 z^5 - 23466240 z^6 + 3322080 z^7 - 362880 z^8 - 9600 z^9 + 90624 z^10 + 99072 z^11 + 19456 z^12 + 1024 z^13))

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]