Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2683)

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=-3/2

http://functions.wolfram.com/07.25.03.2683.01

Input Form

HypergeometricPFQ[{-(11/2), 11/2}, {-(3/2), 6}, z] == (1/(2749862115 z^3)) (32 E^(z/2) (-35675640 + 25041555 z - 12286890 z^2 + 92363040 z^3 + 239057280 z^4 + 1045158912 z^5 - 3280564224 z^6 + 1988493312 z^7 - 379060224 z^8 + 20971520 z^9) BesselI[0, z/2]) - (1/(2749862115 z^4)) (32 E^(z/2) (-142702560 + 100166220 z - 53607015 z^2 + 28849590 z^3 - 28717920 z^4 - 90018432 z^5 - 224695296 z^6 - 1797746688 z^7 + 1640890368 z^8 - 358088704 z^9 + 20971520 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]