Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.al9z)

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=7/2, a₂>=7/2

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

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

http://functions.wolfram.com/07.25.03.al9z.01

Input Form

HypergeometricPFQ[{7/2, 9/2}, {-(7/2), 1}, z] == (1/165375) (E^(z/2) (165375 - 826875 z + 2160900 z^2 - 5638500 z^3 + 31787280 z^4 + 137886000 z^5 + 137921280 z^6 + 57281280 z^7 + 11513600 z^8 + 1164544 z^9 + 56320 z^10 + 1024 z^11) BesselI[0, z/2]) + (1/165375) (E^(z/2) (253575 z - 819000 z^2 + 1931580 z^3 - 5812800 z^4 + 59117520 z^5 + 94832640 z^6 + 47353600 z^7 + 10430464 z^8 + 1109760 z^9 + 55296 z^10 + 1024 z^11) 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]