Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0838)

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=-11/2, a₂>=-11/2

For fixed z and a₁=-11/2, a₂=1/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=1/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.0838.01

Input Form

HypergeometricPFQ[{-(11/2), 1/2}, {-(3/2), 6}, z] == (1/(2749862115 z^3)) (32 E^(z/2) (35675640 + 46995795 z + 38482290 z^2 + 113513400 z^3 + 6985440 z^4 + 15782256 z^5 - 30442272 z^6 + 8106816 z^7 - 724992 z^8 + 20480 z^9) BesselI[0, z/2]) - (1/(2749862115 z^4)) (32 E^(z/2) (142702560 + 187983180 z + 158388615 z^2 + 116195310 z^3 + 99542520 z^4 - 3731616 z^5 - 4513488 z^6 - 23361504 z^7 + 7412544 z^8 - 704512 z^9 + 20480 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]