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

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=9/2, a₂>=9/2

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

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

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

Input Form

HypergeometricPFQ[{9/2, 9/2}, {-(11/2), 5}, z] == (1/(38201625 z^2)) (32 E^(z/2) (1964187225 - 964863900 z + 300623400 z^2 - 70648200 z^3 + 13696200 z^4 - 2459520 z^5 + 564480 z^6 - 314880 z^7 + 725760 z^8 + 1551360 z^9 + 530432 z^10 + 59392 z^11 + 2048 z^12) BesselI[0, z/2]) + (1/(38201625 z^3)) (128 E^(z/2) (-1964187225 + 964863900 z - 360810450 z^2 + 99324225 z^3 - 21407400 z^4 + 3735270 z^5 - 514080 z^6 + 32640 z^7 + 26880 z^8 - 48000 z^9 + 275968 z^10 + 118528 z^11 + 14336 z^12 + 512 z^13) 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]