Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9998)

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=-5/2, a₂>=-5/2

For fixed z and a₁=-5/2, a₂=3, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=3, b₁=4

http://functions.wolfram.com/07.25.03.9998.01

Input Form

HypergeometricPFQ[{-(5/2), 3}, {4, 6}, z] == 320/(77 z^3) - (1/(10405395 z^3)) (64 E^(z/2) (696465 - 270270 z - 57390 z^2 - 189600 z^3 + 107760 z^4 - 15904 z^5 + 672 z^6) BesselI[0, z/2]) + (1/(10405395 z^4)) (128 E^(z/2) (41580 + 135135 z - 197940 z^2 - 63885 z^3 - 51840 z^4 + 46432 z^5 - 7616 z^6 + 336 z^7) 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]