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

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=9/2, b₁>=-11/2

For fixed z and a₁=1/2, a₂=9/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{1/2, 9/2}, {-(11/2), 6}, z] == (1/(72765 z^3)) (32 E^(z/2) (349188840 - 155887875 z + 44633160 z^2 - 9476280 z^3 + 1587600 z^4 - 216048 z^5 + 24000 z^6 - 2112 z^7 + 128 z^8) BesselI[0, z/2]) + (1/(72765 z^4)) (32 E^(z/2) (-1396755360 + 623551500 z - 222181245 z^2 + 57400200 z^3 - 11480040 z^4 + 1846992 z^5 - 243600 z^6 + 26304 z^7 - 2240 z^8 + 128 z^9) 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]