Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2264)

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=9/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=9/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.2264.01

Input Form

HypergeometricPFQ[{-(11/2), 9/2}, {-(5/2), 4}, z] == -((1/(57432375 z)) (4 E^(z/2) (343035 - 14927220 z - 27276480 z^2 - 38288640 z^3 - 116889600 z^4 + 275914752 z^5 - 105119744 z^6 + 9437184 z^7) BesselI[0, z/2])) + (1/(57432375 z^2)) (4 E^(z/2) (1372140 - 2276505 z + 4365900 z^2 + 13830720 z^3 + 17652480 z^4 + 29657088 z^5 + 184950784 z^6 - 95682560 z^7 + 9437184 z^8) 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]