Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1861)

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=7/2, b₁>=-11/2

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

http://functions.wolfram.com/07.25.03.1861.01

Input Form

HypergeometricPFQ[{-(11/2), 7/2}, {-(7/2), 5}, z] == (1/(1091215125 z^2)) (32 E^(z/2) (-200675475 + 57972915 z + 30852360 z^2 + 12972960 z^3 + 6397440 z^4 + 4700160 z^5 + 9289728 z^6 - 15269888 z^7 + 2097152 z^8) BesselI[0, z/2]) - (1/(1091215125 z^3)) (32 E^(z/2) (-802701900 + 231891660 z - 38076885 z^2 - 22702680 z^3 - 9337440 z^4 - 4262400 z^5 - 2623488 z^6 - 2834432 z^7 - 13172736 z^8 + 2097152 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]