Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4561)

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=3, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=3, b₁=6

http://functions.wolfram.com/07.25.03.4561.01

Input Form

HypergeometricPFQ[{-(9/2), 3}, {6, 6}, z] == (1920 (96 - 456 z + 323 z^2))/(46189 z^5) - (1/(2016085416345 z^5)) (512 E^(z/2) (15713497800 - 82495863450 z + 83936573055 z^2 - 14929427520 z^3 - 1940560920 z^4 - 4641144480 z^5 + 2867383440 z^6 - 586121472 z^7 + 54280128 z^8 - 2314752 z^9 + 36608 z^10) BesselI[0, z/2]) + (1/(2016085416345 z^4)) (512 E^(z/2) (-28937802555 + 64026085095 z - 18630708120 z^2 - 3669692040 z^3 - 2507343120 z^4 + 2356026192 z^5 - 535203648 z^6 + 52020288 z^7 - 2278144 z^8 + 36608 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]