Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4097)

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=1/2

http://functions.wolfram.com/07.25.03.4097.01

Input Form

HypergeometricPFQ[{-(9/2), 2}, {1/2, 5}, z] == (12 (42 + 68 z + 51 z^2))/(2431 z^4) + (1/(36465 z^4)) (E^z (-7560 - 4680 z - 720 z^2 + 4320 z^3 + 33600 z^4 - 57261 z^5 + 20262 z^6 - 2404 z^7 + 88 z^8)) + (Sqrt[Pi] (-109395 Sqrt[z] + 132600 z^(3/2) - 42840 z^(5/2) + 4896 z^(7/2) - 176 z^(9/2)) Erfi[Sqrt[z]])/72930

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]