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

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.ajno.01

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(9/2), 3}, z] == -((1/2679075) (4 E^(z/2) (-1176525 + 1134000 z - 850500 z^2 + 705600 z^3 - 831600 z^4 + 2540160 z^5 + 6478080 z^6 + 3127296 z^7 + 559872 z^8 + 40960 z^9 + 1024 z^10) BesselI[0, z/2])) - (1/(2679075 z)) (4 E^(z/2) (2027025 - 467775 z - 283500 z^2 + 409500 z^3 - 378000 z^4 + 388080 z^5 - 631680 z^6 + 4075776 z^7 + 2625792 z^8 + 520448 z^9 + 39936 z^10 + 1024 z^11) 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

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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]
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