Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ae6s)

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=1/2, a₂=11/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.ae6s.01

Input Form

HypergeometricPFQ[{1/2, 11/2}, {-(9/2), 4}, z] == -((1/(297675 z)) (4 E^(z/2) (405405 - 446040 z + 264600 z^2 - 105840 z^3 + 31920 z^4 - 8256 z^5 + 3648 z^6 + 3200 z^7 + 256 z^8) BesselI[0, z/2])) - (1/(297675 z^2)) (4 E^(z/2) (-1621620 + 1486485 z - 914760 z^2 + 415800 z^3 - 142800 z^4 + 38064 z^5 - 7872 z^6 + 832 z^7 + 2944 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]