Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ae7v)

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=1/2, a₂>=1/2

For fixed z and a₁=1/2, a₂=11/2, b₁>=-11/2

For fixed z and a₁=1/2, a₂=11/2, b₁=-3/2

http://functions.wolfram.com/07.25.03.ae7v.01

Input Form

HypergeometricPFQ[{1/2, 11/2}, {-(3/2), 1}, z] == (1/2835) (E^(z/2) (2835 - 6615 z + 27792 z^2 + 93912 z^3 + 67632 z^4 + 17808 z^5 + 1856 z^6 + 64 z^7) BesselI[0, z/2]) + (1/2835) (E^(z/2) (1287 z - 5208 z^2 + 47928 z^3 + 52416 z^4 + 16048 z^5 + 1792 z^6 + 64 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]