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

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.allf.01

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(7/2), 3}, z] == (1/1488375) (4 E^(z/2) (411075 - 850500 z + 1266300 z^2 - 2217600 z^3 + 9167760 z^4 + 30461760 z^5 + 21907200 z^6 + 6266880 z^7 + 817920 z^8 + 48128 z^9 + 1024 z^10) BesselI[0, z/2]) + (1/(1488375 z)) (4 E^(z/2) (-155925 - 70875 z + 378000 z^2 - 598500 z^3 + 902160 z^4 - 1970640 z^5 + 15852480 z^6 + 16730880 z^7 + 5518080 z^8 + 771328 z^9 + 47104 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

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]