Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1980)

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=7/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=7/2, b₁=5/2

http://functions.wolfram.com/07.25.03.1980.01

Input Form

HypergeometricPFQ[{-(11/2), 7/2}, {5/2, 6}, z] == (1/(4583103525 z^3)) (32 E^(z/2) (-1247400 - 1340955 z - 249480 z^2 + 144947880 z^3 - 247983120 z^4 + 139401360 z^5 - 34087872 z^6 + 3945408 z^7 - 210048 z^8 + 4096 z^9) BesselI[0, z/2]) - (1/(4583103525 z^4)) (32 E^(z/2) (-4989600 - 5363820 z - 1153845 z^2 + 6735960 z^3 + 29688120 z^4 - 149420880 z^5 + 110633712 z^6 - 30445248 z^7 + 3741504 z^8 - 205952 z^9 + 4096 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]