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

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=11/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=11/2, b₁=-5/2

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

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(5/2), 3}, z] == -((1/212625) (8 E^(z/2) (-28350 + 80325 z - 194400 z^2 + 984240 z^3 + 3791520 z^4 + 3220560 z^5 + 1075200 z^6 + 161280 z^7 + 10752 z^8 + 256 z^9) BesselI[0, z/2])) - (1/(212625 z)) (4 E^(z/2) (14175 + 9450 z - 60750 z^2 + 139680 z^3 - 383760 z^4 + 3555360 z^5 + 4714080 z^6 + 1858560 z^7 + 301824 z^8 + 20992 z^9 + 512 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]