Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1219)

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=3/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=3/2, b₁=1/2

http://functions.wolfram.com/07.25.03.1219.01

Input Form

HypergeometricPFQ[{-(11/2), 3/2}, {1/2, 6}, z] == (1/(305540235 z^3)) (32 E^(z/2) (-748440 - 1153845 z - 1081080 z^2 + 8731800 z^3 - 31434480 z^4 + 23929584 z^5 - 6877248 z^6 + 879168 z^7 - 50048 z^8 + 1024 z^9) BesselI[0, z/2]) - (1/(305540235 z^4)) (32 E^(z/2) (-2993760 - 4615380 z - 4417875 z^2 - 3409560 z^3 - 1746360 z^4 - 15549744 z^5 + 18229008 z^6 - 6070080 z^7 + 830656 z^8 - 49024 z^9 + 1024 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]