Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.alq0)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=-9/2

http://functions.wolfram.com/07.25.03.alq0.01

Input Form

HypergeometricPFQ[{7/2, 6}, {-(9/2), 11/2}, -z] == (1/(3600 z^4)) (38102400 + 14515200 z + 4415040 z^2 + 1088640 z^3 + 223200 z^4 + 40320 z^5 + 7560 z^6 + 2352 z^7 + 1977 z^8 + 6000 z^9 - 3088 z^10 + 416 z^11 - 16 z^12) + (1/(7200 z^(9/2))) ((Sqrt[Pi] (-38102400 - 39916800 z - 20865600 z^2 - 7257600 z^3 - 1890000 z^4 - 393120 z^5 - 68040 z^6 - 10080 z^7 - 1305 z^8 - 150 z^9 - 14712 z^10 + 6576 z^11 - 848 z^12 + 32 z^13) Erfi[Sqrt[z]])/E^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]