Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9613)

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=2, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=2, b₁=5

http://functions.wolfram.com/07.25.03.9613.01

Input Form

HypergeometricPFQ[{-(5/2), 2}, {5, 6}, z] == (320 (144 - 312 z + 143 z^2))/(3003 z^4) - (1/(405810405 z^4)) (1024 E^(z/2) (6081075 - 16081065 z + 10980360 z^2 - 1533240 z^3 - 578640 z^4 + 178800 z^5 - 15936 z^6 + 448 z^7) BesselI[0, z/2]) + (1/(405810405 z^4)) (1024 E^(z/2) (540540 - 8105535 z + 9002160 z^2 - 1887960 z^3 - 422400 z^4 + 163536 z^5 - 15488 z^6 + 448 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]