Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a8ct)

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=11/2, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=11/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.a8ct.01

Input Form

HypergeometricPFQ[{-(5/2), 11/2}, {-(11/2), 3}, z] == -((1/654885) (4 E^(z/2) (-171765 - 33660 z + 39672 z^2 - 5376 z^3 - 1680 z^4 + 576 z^5 + 64 z^6) BesselI[0, z/2])) - (1/(654885 z)) (4 E^(z/2) (32175 - 83655 z - 73548 z^2 + 41304 z^3 - 3024 z^4 - 2160 z^5 + 512 z^6 + 64 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]