Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ano2)

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=11/2, a₂>=11/2

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

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

http://functions.wolfram.com/07.25.03.ano2.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(9/2), 5}, z] == -((1/(281302875 z^2)) (32 E^(z/2) (-103378275 + 42567525 z - 22283100 z^2 + 18314100 z^3 - 16783200 z^4 + 17146080 z^5 - 23950080 z^6 + 84568320 z^7 + 247968000 z^8 + 151722240 z^9 + 37174272 z^10 + 4205568 z^11 + 217088 z^12 + 4096 z^13) BesselI[0, z/2])) - (1/(281302875 z^3)) (32 E^(z/2) (413513100 - 170270100 z + 66891825 z^2 - 13721400 z^3 - 4706100 z^4 + 8527680 z^5 - 8981280 z^6 + 10575360 z^7 - 19595520 z^8 + 140989440 z^9 + 120237312 z^10 + 33282048 z^11 + 3994624 z^12 + 212992 z^13 + 4096 z^14) 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]