Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.9357)

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=3/2, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=3/2, b₁=-1/2

http://functions.wolfram.com/07.25.03.9357.01

Input Form

HypergeometricPFQ[{-(5/2), 3/2}, {-(1/2), 6}, z] == (1/(45045 z^3)) (32 E^(z/2) (-11880 - 8235 z - 3300 z^2 + 540 z^3 + 1080 z^4 - 1792 z^5 + 256 z^6) BesselI[0, z/2]) - (1/(45045 z^4)) (32 E^(z/2) (-47520 - 32940 z - 14685 z^2 - 4500 z^3 - 300 z^4 - 328 z^5 - 1536 z^6 + 256 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]