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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(7/2), 1}, z] == (1/1488375) (E^(z/2) (1488375 - 8930250 z + 27518400 z^2 - 83235600 z^3 + 536676840 z^4 + 2645808480 z^5 + 3093350400 z^6 + 1550223360 z^7 + 392474880 z^8 + 53386752 z^9 + 3907584 z^10 + 143360 z^11 + 2048 z^12) BesselI[0, z/2]) + (1/1488375) (2 E^(z/2) (1223775 z - 4791150 z^2 + 13226220 z^3 - 45449460 z^4 + 515486160 z^5 + 999411840 z^6 + 613589760 z^7 + 172267776 z^8 + 24844032 z^9 + 1883648 z^10 + 70656 z^11 + 1024 z^12) 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]