Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al9q)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=9/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.al9q.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(9/2), 5}, z] == -((1/(496125 z^2)) (32 E^(z/2) (103378275 - 52702650 z + 16618770 z^2 - 3900960 z^3 + 730800 z^4 - 110880 z^5 + 10080 z^6 + 12288 z^7 + 28416 z^8 + 7680 z^9 + 512 z^10) BesselI[0, z/2])) - (1/(496125 z^3)) (64 E^(z/2) (-206756550 + 105405300 z - 39729690 z^2 + 11133045 z^3 - 2459520 z^4 + 448560 z^5 - 70560 z^6 + 10704 z^7 - 3072 z^8 + 10752 z^9 + 3584 z^10 + 256 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]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]