Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0419)

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=-5/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.0419.01

Input Form

HypergeometricPFQ[{-(11/2), -(5/2)}, {-(7/2), 5}, z] == -((1/(1527701175 z^2)) (32 E^(z/2) (-467775 - 1049895 z - 49480200 z^2 + 57629880 z^3 - 19855920 z^4 + 2244240 z^5 + 9792 z^6 - 13760 z^7 + 512 z^8) BesselI[0, z/2])) + (1/(1527701175 z^3)) (32 E^(z/2) (-1871100 - 4199580 z - 7016625 z^2 - 15135120 z^3 + 41075160 z^4 - 17634240 z^5 + 2234928 z^6 - 3200 z^7 - 13248 z^8 + 512 z^9) 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]