Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4165)

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=-9/2, a₂>=-9/2

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

For fixed z and a₁=-9/2, a₂=2, b₁=4

http://functions.wolfram.com/07.25.03.4165.01

Input Form

HypergeometricPFQ[{-(9/2), 2}, {4, 9/2}, z] == (42 (-2 + 5 z))/(143 z^3) + (1/(70287360 z^3)) (E^z (31152555 - 40452930 z - 19380060 z^2 + 28424520 z^3 - 9047280 z^4 + 1189536 z^5 - 68416 z^6 + 1408 z^7)) + (1/(140574720 z^(7/2))) (Sqrt[Pi] (10135125 - 97297200 z + 75675600 z^2 + 60540480 z^3 - 64864800 z^4 + 19219200 z^5 - 2446080 z^6 + 138240 z^7 - 2816 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]