Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.2523)

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=5, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=5, b₁=2

http://functions.wolfram.com/07.25.03.2523.01

Input Form

HypergeometricPFQ[{-(11/2), 5}, {2, 6}, z] == (1/(916620705 z^3)) (2 E^(z/2) (-997920 + 498960 z - 155925 z^2 + 458346735 z^3 - 1268439480 z^4 + 1077019272 z^5 - 376629456 z^6 + 59501040 z^7 - 4161600 z^8 + 103360 z^9) BesselI[0, z/2]) - (1/(916620705 z^4)) (2 E^(z/2) (-3991680 + 1995840 z - 748440 z^2 + 207900 z^3 + 44022825 z^4 - 607843152 z^5 + 777970536 z^6 - 323060736 z^7 + 55494480 z^8 - 4058240 z^9 + 103360 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]