Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.agw6)

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=9/2, b₁>=-11/2

For fixed z and a₁=3/2, a₂=9/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.agw6.01

Input Form

HypergeometricPFQ[{3/2, 9/2}, {-(5/2), 3}, z] == -((4 E^(z/2) (315 - 360 z^2 + 1344 z^3 + 2928 z^4 + 896 z^5 + 64 z^6) BesselI[0, z/2])/1575) - (1/(1575 z)) (4 E^(z/2) (-2835 + 2205 z - 1080 z^2 + 504 z^3 - 432 z^4 + 2128 z^5 + 832 z^6 + 64 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]