Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a9g0)

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=2, b₁>=-11/2

For fixed z and a₁=-3/2, a₂=2, b₁=6

http://functions.wolfram.com/07.25.03.a9g0.01

Input Form

HypergeometricPFQ[{-(3/2), 2}, {6, 6}, z] == (320 (-128 + 624 z - 572 z^2 + 143 z^3))/(1001 z^5) + (1/(27054027 z^5)) (1024 E^(z/2) (1081080 - 5810805 z + 7039146 z^2 - 2756616 z^3 + 248928 z^4 + 46832 z^5 - 8352 z^6 + 320 z^7) BesselI[0, z/2]) - (1/(27054027 z^4)) (1024 E^(z/2) (-1978521 + 4739286 z - 2459976 z^2 + 284192 z^3 + 38960 z^4 - 8032 z^5 + 320 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]