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

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=9/2, b₁>=-11/2

For fixed z and a₁=1/2, a₂=9/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{1/2, 9/2}, {-(11/2), 5}, z] == (1/(363825 z^2)) (32 E^(z/2) (18706545 - 10501920 z + 3635280 z^2 - 952560 z^3 + 204960 z^4 - 37824 z^5 + 6144 z^6 - 896 z^7 + 128 z^8) BesselI[0, z/2]) + (1/(363825 z^3)) (128 E^(z/2) (-18706545 + 10501920 z - 4208490 z^2 + 1274130 z^3 - 310800 z^4 + 63924 z^5 - 11424 z^6 + 1808 z^7 - 256 z^8 + 32 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]