Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.anq4)

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=1

http://functions.wolfram.com/07.25.03.anq4.01

Input Form

HypergeometricPFQ[{11/2, 11/2}, {1, 5/2}, z] == (1/297675) (E^(z/2) (297675 + 3453030 z + 8920800 z^2 + 8872416 z^3 + 4090176 z^4 + 943008 z^5 + 110208 z^6 + 6144 z^7 + 128 z^8) BesselI[0, z/2]) + (1/297675) (2 E^(z/2) (333585 z + 2035908 z^2 + 2955528 z^3 + 1647528 z^4 + 420816 z^5 + 52128 z^6 + 3008 z^7 + 64 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]