Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajns)

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=5/2, a₂=11/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.ajns.01

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(9/2), 5}, z] == -((1/(893025 z^2)) (32 E^(z/2) (-34459425 + 20270250 z - 7059150 z^2 + 1814400 z^3 - 378000 z^4 + 70560 z^5 - 16800 z^6 + 19200 z^7 + 34560 z^8 + 8704 z^9 + 512 z^10) BesselI[0, z/2])) - (1/(893025 z^3)) (64 E^(z/2) (68918850 - 40540500 z + 16216200 z^2 - 4833675 z^3 + 1134000 z^4 - 216720 z^5 + 33600 z^6 - 3120 z^7 - 1920 z^8 + 13312 z^9 + 4096 z^10 + 256 z^11) 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]