Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.5774)

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=-7/2, a₂>=-7/2

For fixed z and a₁=-7/2, a₂=-7/2, b₁>=-11/2

For fixed z and a₁=-7/2, a₂=-7/2, b₁=-11/2

http://functions.wolfram.com/07.25.03.5774.01

Input Form

HypergeometricPFQ[{-(7/2), -(7/2)}, {-(11/2), 4}, z] == (1/(4459455 z)) (4 E^(z/2) (26775 + 1168020 z - 1073100 z^2 + 253224 z^3 - 17664 z^4 + 256 z^5) BesselI[0, z/2]) - (1/(4459455 z^2)) (4 E^(z/2) (107100 + 212625 z + 423780 z^2 - 845604 z^3 + 235944 z^4 - 17408 z^5 + 256 z^6) 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]