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

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=1/2

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {1/2, 2}, z] == (1/893025) (E^(z/2) (893025 + 26570250 z + 112676760 z^2 + 166239360 z^3 + 110851440 z^4 + 37326240 z^5 + 6649920 z^6 + 625408 z^7 + 28928 z^8 + 512 z^9) BesselI[0, z/2]) + (1/893025) (E^(z/2) (-11025 + 2751210 z + 39319560 z^2 + 95632320 z^3 + 81837840 z^4 + 31531680 z^5 + 6066368 z^6 + 597248 z^7 + 28416 z^8 + 512 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]