Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.adw3)

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=1/2, a₂=9/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.adw3.01

Input Form

HypergeometricPFQ[{1/2, 9/2}, {-(5/2), 1}, z] == (1/1575) (E^(z/2) (1575 - 2205 z + 2700 z^2 - 7896 z^3 - 19920 z^4 - 9296 z^5 - 1408 z^6 - 64 z^7) BesselI[0, z/2]) + (E^(z/2) (225 z - 756 z^2 + 1800 z^3 - 12544 z^4 - 7984 z^5 - 1344 z^6 - 64 z^7) BesselI[1, z/2])/1575

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]