Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1030)

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=3

http://functions.wolfram.com/07.25.03.1030.01

Input Form

HypergeometricPFQ[{-(11/2), 1}, {3, 9/2}, z] == (14 (-1 + 3 z))/(39 z^2) + (1/(345047040 z^3)) (E^z (-2027025 + 88727940 z - 179776800 z^2 + 120344400 z^3 - 36342240 z^4 + 5553600 z^5 - 440832 z^6 + 17152 z^7 - 256 z^8)) + (1/(690094080 z^(7/2))) (Sqrt[Pi] (2027025 + 36486450 z - 291891600 z^2 + 454053600 z^3 - 272432160 z^4 + 77837760 z^5 - 11531520 z^6 + 898560 z^7 - 34560 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]