Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al9m)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=9/2, b₁>=-11/2

For fixed z and a₁=7/2, a₂=9/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.al9m.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(9/2), 3}, z] == -((1/1488375) (4 E^(z/2) (-473445 + 612360 z - 548100 z^2 + 504000 z^3 - 630000 z^4 + 1999872 z^5 + 5263104 z^6 + 2672640 z^7 + 504576 z^8 + 38912 z^9 + 1024 z^10) BesselI[0, z/2])) - (1/(1488375 z)) (4 E^(z/2) (405405 + 31185 z - 291060 z^2 + 308700 z^3 - 277200 z^4 + 291312 z^5 - 489216 z^6 + 3238656 z^7 + 2223360 z^8 + 467200 z^9 + 37888 z^10 + 1024 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]