Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.4951)

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=4, b₁>=-11/2

For fixed z and a₁=-9/2, a₂=4, b₁=6

http://functions.wolfram.com/07.25.03.4951.01

Input Form

HypergeometricPFQ[{-(9/2), 4}, {6, 6}, z] == (15360 (-8 + 19 z))/(46189 z^5) - (1/(2016085416345 z^5)) (256 E^(z/2) (-20951330400 + 60235074900 z - 17852686965 z^2 - 3316122360 z^3 - 1353654360 z^4 - 8705911920 z^5 + 6935088720 z^6 - 1783285824 z^7 + 200147904 z^8 - 10048896 z^9 + 183040 z^10) BesselI[0, z/2]) + (1/(2016085416345 z^4)) (256 E^(z/2) (33345904140 - 24831369765 z - 6636829320 z^2 - 3680221560 z^3 - 3919501200 z^4 + 5423319504 z^5 - 1597662144 z^6 + 190373568 z^7 - 9865856 z^8 + 183040 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]