Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a813)

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=4, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=4, b₁=5

http://functions.wolfram.com/07.25.03.a813.01

Input Form

HypergeometricPFQ[{-(5/2), 4}, {5, 6}, z] == 5120/(1001 z^4) - (1/(135270135 z^4)) (512 E^(z/2) (1351350 - 585585 z - 142500 z^2 - 63885 z^3 - 301920 z^4 + 182560 z^5 - 28224 z^6 + 1232 z^7) BesselI[0, z/2]) + (1/(135270135 z^4)) (256 E^(z/2) (720720 - 1815675 z - 601170 z^2 - 333870 z^3 - 316000 z^4 + 312368 z^5 - 53984 z^6 + 2464 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]