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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{9/2, 11/2}, {-(11/2), 3}, z] == (1/1031443875) (8 E^(z/2) (140332500 - 250259625 z + 265015800 z^2 - 247665600 z^3 + 254016000 z^4 - 362426400 z^5 + 1328140800 z^6 + 4095982080 z^7 + 2753879040 z^8 + 783763200 z^9 + 111175680 z^10 + 8171520 z^11 + 294912 z^12 + 4096 z^13) BesselI[0, z/2]) + (1/(1031443875 z)) (4 E^(z/2) (-91216125 - 60810750 z + 251492850 z^2 - 301417200 z^3 + 282592800 z^4 - 269438400 z^5 + 316612800 z^6 - 602173440 z^7 + 4482190080 z^8 + 4229153280 z^9 + 1367984640 z^10 + 206868480 z^11 + 15765504 z^12 + 581632 z^13 + 8192 z^14) 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]