Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.8990)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=1/2, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=1/2, b₁=-1/2

http://functions.wolfram.com/07.25.03.8990.01

Input Form

HypergeometricPFQ[{-(5/2), 1/2}, {-(1/2), 6}, z] == (32 E^(z/2) (3960 + 4095 z + 2700 z^2 + 5820 z^3 + 840 z^4 - 1296 z^5 + 128 z^6) BesselI[0, z/2])/(135135 z^3) - (1/(135135 z^4)) (32 E^(z/2) (15840 + 16380 z + 11295 z^2 + 6900 z^3 + 5100 z^4 - 264 z^5 - 1168 z^6 + 128 z^7) 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]