Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.acd0)

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=-1/2, a₂>=-1/2

For fixed z and a₁=-1/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=-1/2, a₂=11/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.acd0.01

Input Form

HypergeometricPFQ[{-(1/2), 11/2}, {-(5/2), 6}, z] == (32 E^(z/2) (-4680 + 2769 z - 1020 z^2 + 324 z^3 - 88 z^4 + 16 z^5) BesselI[0, z/2])/(945 z^3) + (1/(945 z^4)) (32 E^(z/2) (18720 - 11076 z + 4665 z^2 - 1524 z^3 + 436 z^4 - 104 z^5 + 16 z^6) 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]