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

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=11/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{-(3/2), 11/2}, {-(11/2), 1}, z] == (1/3274425) (E^(z/2) (3274425 + 3274425 z - 2381400 z^2 + 189000 z^3 + 327600 z^4 - 198480 z^5 + 104640 z^6 + 60864 z^7 + 7424 z^8 + 256 z^9) BesselI[0, z/2]) + (1/3274425) (E^(z/2) (4068225 z - 1587600 z^2 - 441000 z^3 + 552000 z^4 - 232080 z^5 + 54144 z^6 + 53824 z^7 + 7168 z^8 + 256 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]