Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1043)

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=1, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=1, b₁=4

http://functions.wolfram.com/07.25.03.1043.01

Input Form

HypergeometricPFQ[{-(11/2), 1}, {4, 9/2}, z] == (7 (6 - 34 z + 51 z^2))/(221 z^3) + (1/(977633280 z^3)) (E^z (-151335135 + 595387800 z - 648232200 z^2 + 299756160 z^3 - 69463680 z^4 + 8631168 z^5 - 577920 z^6 + 19456 z^7 - 256 z^8)) + (1/(1955266560 z^(7/2))) (Sqrt[Pi] (-34459425 + 620269650 z - 1654052400 z^2 + 1543782240 z^3 - 661620960 z^4 + 147026880 z^5 - 17821440 z^6 + 1175040 z^7 - 39168 z^8 + 512 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]