Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a9r2)

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=-3/2, a₂>=-3/2

For fixed z and a₁=-3/2, a₂=3, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=3, b₁=6

http://functions.wolfram.com/07.25.03.a9r2.01

Input Form

HypergeometricPFQ[{-(3/2), 3}, {6, 6}, z] == (640 (96 - 312 z + 143 z^2))/(1001 z^5) + (1/(27054027 z^5)) (1024 E^(z/2) (-1621620 + 6081075 z - 4477644 z^2 + 574965 z^3 + 50304 z^4 + 38016 z^5 - 10560 z^6 + 560 z^7) BesselI[0, z/2]) - (1/(27054027 z^4)) (512 E^(z/2) (5395023 - 7562430 z + 1310046 z^2 + 148320 z^3 + 56592 z^4 - 20000 z^5 + 1120 z^6) 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]