Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2152)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=4, b₁=7/2

http://functions.wolfram.com/07.25.03.2152.01

Input Form

HypergeometricPFQ[{-(11/2), 4}, {7/2, 5}, z] == -(24/(4199 z^4)) + (1/(7223623680 z^4)) (E^z (41287680 - 41287680 z - 197599185 z^2 - 559763610 z^3 + 4140842580 z^4 - 3283122264 z^5 + 945672144 z^6 - 120784352 z^7 + 6884800 z^8 - 141440 z^9)) + (1/(14447247360 z^(5/2))) (Sqrt[Pi] (218243025 + 698377680 z + 3491888400 z^2 - 10863652800 z^3 + 7407036000 z^4 - 2005597440 z^5 + 248312064 z^6 - 13911040 z^7 + 282880 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]