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

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=-5/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(5/2), 1}, z] == (1/13395375) (E^(z/2) (13395375 - 168781725 z + 1216385100 z^2 - 14786350740 z^3 - 122076188640 z^4 - 238452167520 z^5 - 202315034880 z^6 - 89305493760 z^7 - 22298879232 z^8 - 3276640512 z^9 - 285551616 z^10 - 14355456 z^11 - 380928 z^12 - 4096 z^13) BesselI[0, z/2]) + (1/13395375) (E^(z/2) (27343575 z - 244331640 z^2 + 1730472660 z^3 - 32388128640 z^4 - 122766749280 z^5 - 138531617280 z^6 - 71168170752 z^7 - 19410388992 z^8 - 3011511552 z^9 - 271755264 z^10 - 13980672 z^11 - 376832 z^12 - 4096 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]