Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0422)

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=-5/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=-5/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.0422.01

Input Form

HypergeometricPFQ[{-(11/2), -(5/2)}, {-(7/2), 6}, z] == -((1/(6416344935 z^3)) (32 E^(z/2) (-4241160 - 7702695 z - 9230760 z^2 - 211309560 z^3 + 213055920 z^4 - 63436464 z^5 + 6280512 z^6 + 21696 z^7 - 30336 z^8 + 1024 z^9) BesselI[0, z/2])) + (1/(6416344935 z^4)) (32 E^(z/2) (-16964640 - 30810780 z - 37453185 z^2 - 44157960 z^3 - 75093480 z^4 + 158894064 z^5 - 57206352 z^6 + 6259776 z^7 - 7104 z^8 - 29312 z^9 + 1024 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]