Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ah6v)

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=3/2, a₂>=3/2

For fixed z and a₁=3/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=3/2, a₂=11/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.ah6v.01

Input Form

HypergeometricPFQ[{3/2, 11/2}, {-(9/2), 6}, z] == -((1/(59535 z^3)) (32 E^(z/2) (-149652360 + 81718065 z - 27335880 z^2 + 6826680 z^3 - 1375920 z^4 + 233712 z^5 - 34368 z^6 + 4416 z^7 - 384 z^8 + 256 z^9) BesselI[0, z/2])) - (1/(59535 z^4)) (32 E^(z/2) (598609440 - 326872260 z + 128050065 z^2 - 37528920 z^3 + 8731800 z^4 - 1684368 z^5 + 277872 z^6 - 40128 z^7 + 5184 z^8 - 640 z^9 + 256 z^10) 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]