Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.a85b)

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=9/2, b₁>=-11/2

For fixed z and a₁=-5/2, a₂=9/2, b₁=3/2

http://functions.wolfram.com/07.25.03.a85b.01

Input Form

HypergeometricPFQ[{-(5/2), 9/2}, {3/2, 6}, z] == -((1/(945945 z^3)) (32 E^(z/2) (2520 - 585 z - 90 z^2 - 29340 z^3 + 50880 z^4 - 20736 z^5 + 2048 z^6) BesselI[0, z/2])) + (1/(945945 z^4)) (32 E^(z/2) (10080 - 2340 z - 45 z^2 + 810 z^3 - 3420 z^4 + 33216 z^5 - 18688 z^6 + 2048 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]