Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amm8)

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=9/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.amm8.01

Input Form

HypergeometricPFQ[{9/2, 9/2}, {-(9/2), 6}, z] == -((1/(694575 z^3)) (32 E^(z/2) (-15713497800 + 7753370625 z - 2404051650 z^2 + 556941420 z^3 - 103692960 z^4 + 16173360 z^5 - 2167200 z^6 + 247680 z^7 - 3072 z^8 + 51456 z^9 + 13824 z^10 + 1024 z^11) BesselI[0, z/2])) - (1/(694575 z^4)) (32 E^(z/2) (62853991200 - 31013482500 z + 11580393825 z^2 - 3197023830 z^3 + 694926540 z^4 - 124296480 z^5 + 18874800 z^6 - 2492640 z^7 + 294528 z^8 - 36864 z^9 + 39168 z^10 + 12800 z^11 + 1024 z^12) 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]