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

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=9/2, b₁=-5/2

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

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(5/2), 4}, z] == -((1/(7875 z)) (4 E^(z/2) (-10395 + 2520 z + 2520 z^2 - 6000 z^3 + 22320 z^4 + 61632 z^5 + 31808 z^6 + 5248 z^7 + 256 z^8) BesselI[0, z/2])) - (1/(7875 z^2)) (4 E^(z/2) (41580 - 17955 z + 7560 z^2 - 3720 z^3 + 3120 z^4 - 5328 z^5 + 36928 z^6 + 26944 z^7 + 4992 z^8 + 256 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]