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

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.alaf.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(5/2), 1}, z] == (1/23625) (E^(z/2) (23625 - 160650 z + 679950 z^2 - 5146560 z^3 - 27448560 z^4 - 33428640 z^5 - 16595040 z^6 - 3912960 z^7 - 456448 z^8 - 25088 z^9 - 512 z^10) BesselI[0, z/2]) - (1/23625) (2 E^(z/2) (-19800 z + 94005 z^2 - 403920 z^3 + 5075760 z^4 + 10758720 z^5 + 6647760 z^6 + 1746304 z^7 + 216064 z^8 + 12288 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]