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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=5/2, a₂=9/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{5/2, 9/2}, {-(11/2), 5}, z] == (1/(1091475 z^2)) (32 E^(z/2) (654729075 - 344594250 z + 111330450 z^2 - 26762400 z^3 + 5166000 z^4 - 836640 z^5 + 117600 z^6 - 15360 z^7 + 3840 z^8 + 3584 z^9 + 512 z^10) BesselI[0, z/2]) + (1/(1091475 z^3)) (64 E^(z/2) (-1309458150 + 689188500 z - 263513250 z^2 + 74999925 z^3 - 16833600 z^4 + 3109680 z^5 - 487200 z^6 + 66000 z^7 - 7680 z^8 + 512 z^9 + 1536 z^10 + 256 z^11) 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]