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

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=-7/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(7/2), 2}, z] == (1/93767625) (E^(z/2) (93767625 - 449489250 z + 1315723500 z^2 - 4046338800 z^3 + 27304633440 z^4 + 143068524480 z^5 + 182096812800 z^6 + 102297323520 z^7 + 30088316160 z^8 + 4983455232 z^9 + 476058624 z^10 + 25743360 z^11 + 724992 z^12 + 8192 z^13) BesselI[0, z/2]) + (1/93767625) (E^(z/2) (-10418625 + 136335150 z - 461821500 z^2 + 1264137840 z^3 - 4485287520 z^4 + 53164278720 z^5 + 113116227840 z^6 + 78440140800 z^7 + 25747206912 z^8 + 4543901184 z^9 + 451378176 z^10 + 25030656 z^11 + 716800 z^12 + 8192 z^13) 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]