Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0310)

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=-7/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=-7/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.0310.01

Input Form

HypergeometricPFQ[{-(11/2), -(7/2)}, {-(9/2), 4}, z] == -((1/(103378275 z)) (4 E^(z/2) (-155925 - 26340930 z + 39002040 z^2 - 17997120 z^3 + 3214320 z^4 - 202080 z^5 - 192 z^6 + 256 z^7) BesselI[0, z/2])) + (1/(103378275 z^2)) (4 E^(z/2) (-623700 - 1985445 z - 6257790 z^2 + 25225560 z^3 - 15084480 z^4 + 3012720 z^5 - 201888 z^6 + 64 z^7 + 256 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]