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

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=-9/2

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

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(9/2), 2}, z] == (1/13395375) (E^(z/2) (13395375 - 34530300 z + 51200100 z^2 - 70119000 z^3 + 122320800 z^4 - 521337600 z^5 - 1821576960 z^6 - 1434585600 z^7 - 475372800 z^8 - 77644800 z^9 - 6497280 z^10 - 264192 z^11 - 4096 z^12) BesselI[0, z/2]) + (1/13395375) (E^(z/2) (-3274425 + 15479100 z - 25533900 z^2 + 33831000 z^3 - 49442400 z^4 + 109751040 z^5 - 911635200 z^6 - 1058158080 z^7 - 406713600 z^8 - 71531520 z^9 - 6239232 z^10 - 260096 z^11 - 4096 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]