Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a8fw)

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=-5/2, a₂>=-5/2

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

For fixed z and a₁=-5/2, a₂=11/2, b₁=1/2

http://functions.wolfram.com/07.25.03.a8fw.01

Input Form

HypergeometricPFQ[{-(5/2), 11/2}, {1/2, 5}, z] == -((1/(945945 z^2)) (32 E^(z/2) (-105 + 150 z - 29760 z^2 + 177920 z^3 - 154624 z^4 + 28672 z^5) BesselI[0, z/2])) + (1/(945945 z^3)) (64 E^(z/2) (-210 + 300 z - 405 z^2 + 1120 z^3 + 33152 z^4 - 62976 z^5 + 14336 z^6) 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]