Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1418)

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=2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=2, b₁=6

http://functions.wolfram.com/07.25.03.1418.01

Input Form

HypergeometricPFQ[{-(11/2), 2}, {6, 6}, z] == (320 (-384 + 3024 z - 4788 z^2 + 2261 z^3))/(88179 z^5) + (1/(80826697146195 z^5)) (1024 E^(z/2) (109994484600 - 921203808525 z + 1754937952110 z^2 - 1148805553140 z^3 + 172556546400 z^4 + 102871576080 z^5 - 49839703200 z^6 + 9250327296 z^7 - 892652544 z^8 + 46775040 z^9 - 1251840 z^10 + 13312 z^11) BesselI[0, z/2]) - (1/(80826697146195 z^4)) (1024 E^(z/2) (-226134864585 + 950333052690 z - 917919100980 z^2 + 222512885280 z^3 + 64565539920 z^4 - 41797528416 z^5 + 8424186624 z^6 - 847715328 z^7 + 45543168 z^8 - 1238528 z^9 + 13312 z^10) 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]