Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2712)

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=11/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.2712.01

Input Form

HypergeometricPFQ[{-(11/2), 11/2}, {1/2, 3}, z] == (1/2027025) (8 E^(z/2) (253440 - 5237595 z + 14841720 z^2 - 13575360 z^3 + 4884480 z^4 - 700416 z^5 + 32768 z^6) BesselI[0, z/2]) - (1/(2027025 z)) (4 E^(z/2) (495 - 8910 z - 1473030 z^2 + 13499760 z^3 - 19286400 z^4 + 8466432 z^5 - 1335296 z^6 + 65536 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]