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

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.ajnm.01

Input Form

HypergeometricPFQ[{5/2, 11/2}, {-(9/2), 2}, z] == (1/2679075) (E^(z/2) (2679075 - 5159700 z + 5953500 z^2 - 6615000 z^3 + 9651600 z^4 - 35118720 z^5 - 105557760 z^6 - 66845184 z^7 - 16950528 z^8 - 1981440 z^9 - 105472 z^10 - 2048 z^11) BesselI[0, z/2]) + (1/2679075) (E^(z/2) (-1091475 + 2778300 z - 3307500 z^2 + 3465000 z^3 - 4208400 z^4 + 8023680 z^5 - 58969344 z^6 - 52566528 z^7 - 15121152 z^8 - 1879040 z^9 - 103424 z^10 - 2048 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

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]
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