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

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=11/2, b₁>=-11/2

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

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

Input Form

HypergeometricPFQ[{11/2, 11/2}, {3/2, 3}, z] == (1/893025) (32 E^(z/2) (27900 + 173475 z + 291600 z^2 + 197610 z^3 + 61824 z^4 + 9288 z^5 + 640 z^6 + 16 z^7) BesselI[0, z/2]) + (1/(893025 z)) (4 E^(z/2) (225 + 5400 z + 404640 z^2 + 1307760 z^3 + 1183392 z^4 + 427584 z^5 + 69376 z^6 + 4992 z^7 + 128 z^8) 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]