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

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=-5/2

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

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(5/2), 4}, z] == -((1/(14175 z)) (4 E^(z/2) (31185 - 22680 z + 12600 z^2 - 10800 z^3 + 30960 z^4 + 80064 z^5 + 38208 z^6 + 5760 z^7 + 256 z^8) BesselI[0, z/2])) - (1/(14175 z^2)) (4 E^(z/2) (-124740 + 76545 z - 27720 z^2 + 5400 z^3 + 2160 z^4 - 7056 z^5 + 49728 z^6 + 32832 z^7 + 5504 z^8 + 256 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]