Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4178)

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=2, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=2, b₁=5

http://functions.wolfram.com/07.25.03.4178.01

Input Form

HypergeometricPFQ[{-(9/2), 2}, {5, 6}, z] == (192 (48 - 136 z + 85 z^2))/(2431 z^4) - (1/(530548793775 z^4)) (1024 E^(z/2) (1964187225 - 6512831325 z + 5672059560 z^2 - 987964200 z^3 - 667308240 z^4 + 325230480 z^5 - 56911680 z^6 + 4750656 z^7 - 188160 z^8 + 2816 z^9) BesselI[0, z/2]) + (1/(530548793775 z^4)) (1024 E^(z/2) (137837700 - 2846195685 z + 4318405200 z^2 - 1305496440 z^3 - 414599040 z^4 + 274902480 z^5 - 52434816 z^6 + 4566720 z^7 - 185344 z^8 + 2816 z^9) 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]