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

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=7/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{7/2, 7/2}, {-(11/2), 4}, z] == (1/(779625 z)) (4 E^(z/2) (34459425 - 16528050 z + 5000940 z^2 - 1113120 z^3 + 183600 z^4 - 12960 z^5 - 13440 z^6 + 39936 z^7 + 76032 z^8 + 17920 z^9 + 1024 z^10) BesselI[0, z/2]) + (1/(779625 z^2)) (4 E^(z/2) (-137837700 + 66891825 z - 25135110 z^2 + 7003980 z^3 - 1550880 z^4 + 293040 z^5 - 54240 z^6 + 14976 z^7 - 12288 z^8 + 59648 z^9 + 16896 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]