Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2611)

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/07.25.03.2611.01

Input Form

HypergeometricPFQ[{-(11/2), 11/2}, {-(9/2), 6}, z] == -((1/(57747104415 z^3)) (32 E^(z/2) (11523231720 - 7353641295 z + 3041348310 z^2 - 2905943040 z^3 - 596090880 z^4 - 154828800 z^5 - 55050240 z^6 - 31457280 z^7 - 50331648 z^8 + 67108864 z^9) BesselI[0, z/2])) + (1/(57747104415 z^4)) (32 E^(z/2) (46092926880 - 29414565180 z + 13605797205 z^2 - 5324589270 z^3 + 2458874880 z^4 + 487710720 z^5 + 120422400 z^6 + 39321600 z^7 + 18874368 z^8 + 16777216 z^9 + 67108864 z^10) 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]