Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1053)

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=1, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=1, b₁=5

http://functions.wolfram.com/07.25.03.1053.01

Input Form

HypergeometricPFQ[{-(11/2), 1}, {5, 5}, z] == (32 (-96 + 912 z - 1938 z^2 + 1615 z^3))/(20995 z^4) + (1/(4582012309875 z^4)) (1024 E^(z/2) (654729075 - 6547290750 z + 16019050770 z^2 - 16150111200 z^3 + 8117596080 z^4 - 2234625120 z^5 + 353320800 z^6 - 32529408 z^7 + 1703680 z^8 - 46592 z^9 + 512 z^10) BesselI[0, z/2]) - (1/(4582012309875 z^3)) (2048 E^(z/2) (-698352210 + 3709876725 z - 5269929120 z^2 + 3163791600 z^3 - 962670240 z^4 + 161605584 z^5 - 15447040 z^6 + 828928 z^7 - 23040 z^8 + 256 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]