Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4927)

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=4, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=4, b₁=3

http://functions.wolfram.com/07.25.03.4927.01

Input Form

HypergeometricPFQ[{-(9/2), 4}, {3, 6}, z] == -((1/(43648605 z^3)) (32 E^(z/2) (15120 + 10395 z - 6615 z^2 - 1393560 z^3 + 1958040 z^4 - 869712 z^5 + 157968 z^6 - 12096 z^7 + 320 z^8) BesselI[0, z/2])) + (1/(43648605 z^4)) (32 E^(z/2) (60480 + 41580 z - 24570 z^2 - 116865 z^3 - 352800 z^4 + 1291512 z^5 - 728928 z^6 + 146352 z^7 - 11776 z^8 + 320 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]