Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.amn5)

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=9/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.amn5.01

Input Form

HypergeometricPFQ[{9/2, 9/2}, {-(5/2), 6}, z] == -((1/(11025 z^3)) (32 E^(z/2) (-48648600 + 23918895 z - 7401240 z^2 + 1711080 z^3 - 317520 z^4 + 48720 z^5 - 4032 z^6 + 7104 z^7 + 2432 z^8 + 256 z^9) BesselI[0, z/2])) - (1/(11025 z^4)) (32 E^(z/2) (194594400 - 95675580 z + 35686035 z^2 - 9835560 z^3 + 2134440 z^4 - 381360 z^5 + 58128 z^6 - 8256 z^7 + 5056 z^8 + 2176 z^9 + 256 z^10) 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]