Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1784)

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=3, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=3, b₁=5

http://functions.wolfram.com/07.25.03.1784.01

Input Form

HypergeometricPFQ[{-(11/2), 3}, {5, 5}, z] == (1536 (-6 + 19 z))/(20995 z^4) + (1/(4582012309875 z^4)) (256 E^(z/2) (7856748900 - 28808079300 z + 9559197315 z^2 + 2269167120 z^3 + 19309317480 z^4 - 18938119680 z^5 + 6488663760 z^6 - 1046372736 z^7 + 85083072 z^8 - 3341312 z^9 + 49920 z^10) BesselI[0, z/2]) - (1/(4582012309875 z^3)) (256 E^(z/2) (-13486807665 + 14969230155 z + 6330130200 z^2 + 7550813880 z^3 - 13788730800 z^4 + 5560284816 z^5 - 966151872 z^6 + 81816640 z^7 - 3291392 z^8 + 49920 z^9) 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]