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

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=-11/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(11/2), 6}, z] == (1/(618866325 z^3)) (32 E^(z/2) (329983453800 - 163027539675 z + 50655354750 z^2 - 11733668100 z^3 + 2167981200 z^4 - 325049760 z^5 + 34292160 z^6 + 3628800 z^7 - 9400320 z^8 + 28627200 z^9 + 69459456 z^10 + 30802944 z^11 + 5099520 z^12 + 348160 z^13 + 8192 z^14) BesselI[0, z/2]) + (1/(618866325 z^4)) (32 E^(z/2) (-1319933815200 + 652110158700 z - 243869350725 z^2 + 67390473150 z^3 - 14683769100 z^4 + 2644896240 z^5 - 411596640 z^6 + 60419520 z^7 - 11508480 z^8 + 5483520 z^9 - 7405824 z^10 + 45325824 z^11 + 26201088 z^12 + 4763648 z^13 + 339968 z^14 + 8192 z^15) 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]