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

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=4, a₂>=4

For fixed z and a₁=4, a₂=11/2, b₁>=-11/2

For fixed z and a₁=4, a₂=11/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{4, 11/2}, {-(11/2), 6}, z] == (167960 (-84 + z))/(21 z^5) + (1/(1964655 z^5)) (4 E^z (329983453800 - 333911828250 z + 168920101350 z^2 - 56961429525 z^3 + 14404039650 z^4 - 2913053220 z^5 + 490228200 z^6 - 70187040 z^7 + 8458560 z^8 - 696960 z^9 - 109824 z^10 + 280320 z^11 + 256512 z^12 + 44032 z^13 + 2048 z^14))

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]