Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ah71)

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=11/2, b₁>=-11/2

For fixed z and a₁=3/2, a₂=11/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.ah71.01

Input Form

HypergeometricPFQ[{3/2, 11/2}, {-(7/2), 1}, z] == (1/99225) (E^(z/2) (99225 - 283500 z + 475650 z^2 - 889200 z^3 + 3836880 z^4 + 13161600 z^5 + 9823200 z^6 + 2905728 z^7 + 390400 z^8 + 23552 z^9 + 512 z^10) BesselI[0, z/2]) + (1/99225) (2 E^(z/2) (55125 z - 106875 z^2 + 176040 z^3 - 403920 z^4 + 3348720 z^5 + 3718224 z^6 + 1274560 z^7 + 183808 z^8 + 11520 z^9 + 256 z^10) 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]