Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1907)

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=-3/2

http://functions.wolfram.com/07.25.03.1907.01

Input Form

HypergeometricPFQ[{-(11/2), 7/2}, {-(3/2), 5}, z] == (1/(654729075 z^2)) (32 E^(z/2) (-21611205 + 4584195 z + 21663180 z^2 + 39792060 z^3 + 148052160 z^4 - 418515456 z^5 + 222572544 z^6 - 37330944 z^7 + 1835008 z^8) BesselI[0, z/2]) - (1/(654729075 z^3)) (32 E^(z/2) (-86444820 + 18336780 z + 2110185 z^2 - 9397080 z^3 - 16647300 z^4 - 34146624 z^5 - 246434304 z^6 + 187994112 z^7 - 35495936 z^8 + 1835008 z^9) 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]