Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4167)

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=4

http://functions.wolfram.com/07.25.03.4167.01

Input Form

HypergeometricPFQ[{-(9/2), 2}, {4, 5}, z] == (96 (-8 + 15 z))/(715 z^3) - (1/(8212829625 z^3)) (256 E^(z/2) (-34459425 + 81081000 z - 23122980 z^2 - 37312560 z^3 + 26145000 z^4 - 6431040 z^5 + 723360 z^6 - 37248 z^7 + 704 z^8) BesselI[0, z/2]) + (1/(8212829625 z^3)) (128 E^(z/2) (-6081075 + 90691560 z - 71473680 z^2 - 37836720 z^3 + 41385600 z^4 - 11522880 z^5 + 1374336 z^6 - 73088 z^7 + 1408 z^8) 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]