Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0835)

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/07.25.03.0835.01

Input Form

HypergeometricPFQ[{-(11/2), 1/2}, {-(3/2), 5}, z] == (1/(654729075 z^2)) (32 E^(z/2) (3087315 + 4677750 z + 25176690 z^2 + 2328480 z^3 + 5515920 z^4 - 11113824 z^5 + 3305760 z^6 - 328704 z^7 + 10240 z^8) BesselI[0, z/2]) - (1/(654729075 z^3)) (64 E^(z/2) (6174630 + 9355500 z + 9625770 z^2 + 10405395 z^3 - 610560 z^4 - 772368 z^5 - 4135200 z^6 + 1496208 z^7 - 159232 z^8 + 5120 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]