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

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=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(11/2), 6}, z] == (1/(1964655 z^3)) (32 E^(z/2) (-21998896920 + 11654177535 z - 3790536750 z^2 + 917961660 z^3 - 178627680 z^4 + 29154384 z^5 - 4106592 z^6 + 510720 z^7 - 58368 z^8 + 9984 z^9 + 6656 z^10 + 1024 z^11) BesselI[0, z/2]) + (1/(1964655 z^4)) (32 E^(z/2) (87995587680 - 46616710140 z + 17912009115 z^2 - 5128373250 z^3 + 1159458300 z^4 - 216076896 z^5 + 34222608 z^6 - 4710048 z^7 + 572160 z^8 - 61440 z^9 + 4864 z^10 + 5632 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]