Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3939)

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=-9/2, a₂>=-9/2

For fixed z and a₁=-9/2, a₂=3/2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=3/2, b₁=-1/2

http://functions.wolfram.com/07.25.03.3939.01

Input Form

HypergeometricPFQ[{-(9/2), 3/2}, {-(1/2), 3}, z] == (16 E^(z/2) (7560 + 33075 z - 103368 z^2 + 62178 z^3 - 11712 z^4 + 640 z^5) BesselI[0, z/2])/135135 - (1/(135135 z)) (4 E^(z/2) (-14175 - 11340 z - 28488 z^2 - 227352 z^3 + 205704 z^4 - 44288 z^5 + 2560 z^6) 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]