Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a84p)

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=9/2, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=9/2, b₁=1/2

http://functions.wolfram.com/07.25.03.a84p.01

Input Form

HypergeometricPFQ[{-(5/2), 9/2}, {1/2, 5}, z] == -((32 E^(z/2) (-315 + 255 z - 10032 z^2 + 49536 z^3 - 37888 z^4 + 6144 z^5) BesselI[0, z/2])/(315315 z^2)) + (1/(315315 z^3)) (32 E^(z/2) (-1260 + 1020 z - 753 z^2 + 1104 z^3 + 20864 z^4 - 31744 z^5 + 6144 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]