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

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=5/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{5/2, 5/2}, {-(11/2), 3}, z] == (1/93555) (4 E^(z/2) (530145 - 257040 z + 79416 z^2 - 19008 z^3 + 4080 z^4 - 1152 z^5 + 1344 z^6 + 2048 z^7 + 256 z^8) BesselI[0, z/2]) + (1/(93555 z)) (4 E^(z/2) (-2027025 + 945945 z - 345384 z^2 + 93672 z^3 - 19632 z^4 + 3120 z^5 - 192 z^6 - 320 z^7 + 1792 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]