Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1014)

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=2

http://functions.wolfram.com/07.25.03.1014.01

Input Form

HypergeometricPFQ[{-(11/2), 1}, {2, 5}, z] == 8/(13 z) + (1/(2837159325 z^2)) (32 E^(z/2) (-135135 - 55135080 z + 113513400 z^2 - 81070800 z^3 + 26599920 z^4 - 4426944 z^5 + 381248 z^6 - 16000 z^7 + 256 z^8) BesselI[0, z/2]) - (1/(2837159325 z^3)) (32 E^(z/2) (-540540 - 2297295 z - 9729720 z^2 + 61662360 z^3 - 60086640 z^4 + 22698864 z^5 - 4068928 z^6 + 365632 z^7 - 15744 z^8 + 256 z^9) BesselI[1, z/2])

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]