Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ama6)

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=-11/2

http://functions.wolfram.com/07.25.03.ama6.01

Input Form

HypergeometricPFQ[{4, 11/2}, {-(11/2), 3/2}, -z] == (1/29469825) (29469825 + 78586200 z + 113513400 z^2 + 138996000 z^3 + 183783600 z^4 + 338607360 z^5 + 1640943360 z^6 - 2277227520 z^7 + 1013633280 z^8 - 213143040 z^9 + 23705088 z^10 - 1420672 z^11 + 43008 z^12 - 512 z^13) + (1/29469825) ((64 Sqrt[Pi] z^(13/2) (-38372400 + 42209640 z - 17342820 z^2 + 3505260 z^3 - 381165 z^4 + 22530 z^5 - 676 z^6 + 8 z^7) 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]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]