Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4154)

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=3

http://functions.wolfram.com/07.25.03.4154.01

Input Form

HypergeometricPFQ[{-(9/2), 2}, {3, 5}, z] == 96/(143 z^2) - (1/(1642565925 z^2)) (64 E^(z/2) (17432415 - 7567560 z - 28168200 z^2 + 25435440 z^3 - 7847760 z^4 + 1068096 z^5 - 64704 z^6 + 1408 z^7) BesselI[0, z/2]) + (1/(1642565925 z^3)) (64 E^(z/2) (810810 + 4189185 z - 14294520 z^2 - 11771640 z^3 + 19006800 z^4 - 6872496 z^5 + 1005504 z^6 - 63296 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]