Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1930)

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=7/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=7/2, b₁=-1/2

http://functions.wolfram.com/07.25.03.1930.01

Input Form

HypergeometricPFQ[{-(11/2), 7/2}, {-(1/2), 6}, z] == -((1/(130945815 z^3)) (32 E^(z/2) (8232840 + 1777545 z - 623700 z^2 - 4199580 z^3 - 23866920 z^4 + 89973648 z^5 - 69470976 z^6 + 18723840 z^7 - 1941504 z^8 + 65536 z^9) BesselI[0, z/2])) + (1/(130945815 z^4)) (32 E^(z/2) (32931360 + 7110180 z - 1465695 z^2 - 207900 z^3 + 1288980 z^4 + 4551912 z^5 + 43280016 z^6 - 53462784 z^7 + 16880640 z^8 - 1875968 z^9 + 65536 z^10) 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]