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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {-(9/2), 2}, z] == (1/843908625) (E^(z/2) (843908625 - 3229773750 z + 6891771600 z^2 - 12992918400 z^3 + 30086834400 z^4 - 165887870400 z^5 - 742523241600 z^6 - 806699658240 z^7 - 391355677440 z^8 - 100686620160 z^9 - 14764001280 z^10 - 1262100480 z^11 - 61648896 z^12 - 1581056 z^13 - 16384 z^14) BesselI[0, z/2]) + (1/843908625) (E^(z/2) (-114604875 + 1143667350 z - 2919596400 z^2 + 5466787200 z^3 - 10673661600 z^4 + 30344932800 z^5 - 309349031040 z^6 - 530533463040 z^7 - 309473498880 z^8 - 87642831360 z^9 - 13589760000 z^10 - 1202774016 z^11 - 60092416 z^12 - 1564672 z^13 - 16384 z^14) 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]