Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3774)

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=1, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=1, b₁=5/2

http://functions.wolfram.com/07.25.03.3774.01

Input Form

HypergeometricPFQ[{-(9/2), 1}, {5/2, 4}, z] == (3 (-2 - 30 z + 195 z^2))/(715 z^3) + (1/(1372800 z^3)) (E^z (11520 + 161280 z - 614565 z^2 + 508410 z^3 - 160920 z^4 + 22704 z^5 - 1424 z^6 + 32 z^7)) + (1/(2745600 z^(3/2))) (Sqrt[Pi] (-675675 + 1621620 z - 1158300 z^2 + 343200 z^3 - 46800 z^4 + 2880 z^5 - 64 z^6) 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]