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

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=7/2, a₂>=7/2

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

For fixed z and a₁=7/2, a₂=11/2, b₁=-9/2

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

Input Form

HypergeometricPFQ[{7/2, 11/2}, {-(9/2), 1}, z] == (1/13395375) (E^(z/2) (13395375 - 64000125 z + 144074700 z^2 - 267642900 z^3 + 593460000 z^4 - 3091586400 z^5 - 12956832000 z^6 - 12843290880 z^7 - 5524727040 z^8 - 1217491200 z^9 - 146058240 z^10 - 9538560 z^11 - 315392 z^12 - 4096 z^13) BesselI[0, z/2]) + (1/13395375) (E^(z/2) (20539575 z - 60593400 z^2 + 114326100 z^3 - 215913600 z^4 + 585194400 z^5 - 5675604480 z^6 - 8773712640 z^7 - 4500080640 z^8 - 1084826880 z^9 - 136980480 z^10 - 9229312 z^11 - 311296 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]