Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ah6n)

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=3/2, a₂>=3/2

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

For fixed z and a₁=3/2, a₂=11/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.ah6n.01

Input Form

HypergeometricPFQ[{3/2, 11/2}, {-(9/2), 2}, z] == (1/893025) (E^(z/2) (893025 - 992250 z + 850500 z^2 - 756000 z^3 + 903600 z^4 - 2737440 z^5 - 6900480 z^6 - 3268608 z^7 - 575232 z^8 - 41472 z^9 - 1024 z^10) BesselI[0, z/2]) + (1/893025) (E^(z/2) (-1091475 + 992250 z - 661500 z^2 + 468000 z^3 - 435600 z^4 + 686880 z^5 - 4378368 z^6 - 2752512 z^7 - 535296 z^8 - 40448 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]