Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1388)

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=-11/2, a₂>=-11/2

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

For fixed z and a₁=-11/2, a₂=2, b₁=3

http://functions.wolfram.com/07.25.03.1388.01

Input Form

HypergeometricPFQ[{-(11/2), 2}, {3, 4}, z] == 16/(65 z^2) + (1/(2239862625 z^2)) (16 E^(z/2) (-34459425 + 16216200 z + 147147120 z^2 - 187086960 z^3 + 85003200 z^4 - 17893440 z^5 + 1856640 z^6 - 91008 z^7 + 1664 z^8) BesselI[0, z/2]) - (1/(2239862625 z^2)) (32 E^(z/2) (-2027025 + 18618840 z + 23122980 z^2 - 62012880 z^3 + 34817400 z^4 - 8084160 z^5 + 884064 z^6 - 44672 z^7 + 832 z^8) 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]