Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ae6f)

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=-11/2

http://functions.wolfram.com/07.25.03.ae6f.01

Input Form

HypergeometricPFQ[{1/2, 11/2}, {-(11/2), 6}, z] == (1/(654885 z^3)) (32 E^(z/2) (-349188840 + 193300965 z - 65637000 z^2 + 16746840 z^3 - 3492720 z^4 + 625968 z^5 - 99648 z^6 + 14400 z^7 - 1920 z^8 + 256 z^9) BesselI[0, z/2]) + (1/(654885 z^4)) (32 E^(z/2) (1396755360 - 773203860 z + 306196605 z^2 - 91068120 z^3 + 21673080 z^4 - 4333392 z^5 + 754992 z^6 - 117696 z^7 + 16704 z^8 - 2176 z^9 + 256 z^10) 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]