Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2167)

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=-11/2, a₂>=-11/2

For fixed z and a₁=-11/2, a₂=4, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=4, b₁=5

http://functions.wolfram.com/07.25.03.2167.01

Input Form

HypergeometricPFQ[{-(11/2), 4}, {5, 5}, z] == 3072/(20995 z^4) + (1/(4582012309875 z^4)) (128 E^(z/2) (-5237832600 + 2618916300 z + 1265707665 z^2 + 1222211880 z^3 + 37264980600 z^4 - 46582151280 z^5 + 19912416240 z^6 - 3876031296 z^7 + 370314048 z^8 - 16731520 z^9 + 282880 z^10) BesselI[0, z/2]) - (1/(4582012309875 z^3)) (128 E^(z/2) (6372288810 + 5107090545 z + 6023431080 z^2 + 11421406200 z^3 - 31496962800 z^4 + 16543889136 z^5 - 3529965888 z^6 + 354006848 z^7 - 16448640 z^8 + 282880 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]