Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a8d6)

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=-9/2

http://functions.wolfram.com/07.25.03.a8d6.01

Input Form

HypergeometricPFQ[{-(5/2), 11/2}, {-(9/2), 1}, z] == (1/59535) (E^(z/2) (59535 + 152145 z + 16632 z^2 - 43176 z^3 + 6000 z^4 + 8976 z^5 + 1472 z^6 + 64 z^7) BesselI[0, z/2]) + (1/59535) (E^(z/2) (91287 z + 51744 z^2 - 39624 z^3 - 960 z^4 + 7600 z^5 + 1408 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]