Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4168)

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/07.25.03.4168.01

Input Form

HypergeometricPFQ[{-(9/2), 2}, {4, 11/2}, z] == (126 (-2 + 3 z))/(143 z^3) + (1/(281149440 z^4)) (E^z (-14189175 + 322479360 z - 245117880 z^2 - 94500000 z^3 + 104427840 z^4 - 27367680 z^5 + 3069312 z^6 - 154112 z^7 + 2816 z^8)) + (1/(562298880 z^(9/2))) (Sqrt[Pi] (14189175 + 182432250 z - 875674800 z^2 + 454053600 z^3 + 272432160 z^4 - 233513280 z^5 + 57657600 z^6 - 6289920 z^7 + 311040 z^8 - 5632 z^9) 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]