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

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=7/2, b₁>=-11/2

For fixed z and a₁=-1/2, a₂=7/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{-(1/2), 7/2}, {-(11/2), 1}, z] == (1/155925) (E^(z/2) (155925 - 28350 z - 46800 z^2 + 36000 z^3 - 14400 z^4 + 4320 z^5 - 1920 z^6 - 1536 z^7 - 128 z^8) BesselI[0, z/2]) - (1/155925) (2 E^(z/2) (-51075 z + 53100 z^2 - 27000 z^3 + 9000 z^4 - 2160 z^5 + 288 z^6 + 704 z^7 + 64 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]