Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.3439)

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=-9/2, a₂>=-9/2

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

For fixed z and a₁=-9/2, a₂=-1/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.3439.01

Input Form

HypergeometricPFQ[{-(9/2), -(1/2)}, {-(3/2), 6}, z] == (1/(43648605 z^3)) (32 E^(z/2) (98280 + 148365 z + 145530 z^2 + 1499400 z^3 - 846720 z^4 - 37488 z^5 + 59616 z^6 - 7488 z^7 + 256 z^8) BesselI[0, z/2]) - (1/(43648605 z^4)) (32 E^(z/2) (393120 + 593460 z + 594405 z^2 + 560070 z^3 + 723240 z^4 - 815232 z^5 + 11664 z^6 + 52512 z^7 - 7232 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]