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

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=5/2, a₂>=5/2

For fixed z and a₁=5/2, a₂=6, b₁>=-11/2

For fixed z and a₁=5/2, a₂=6, b₁=-7/2

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

Input Form

HypergeometricPFQ[{5/2, 6}, {-(7/2), -(7/2)}, z] == (1/496125) (496125 + 607500 z + 1190700 z^2 + 6350400 z^3 + 314344800 z^4 + 12355200000 z^5 + 47891376000 z^6 + 61559904960 z^7 + 36640293120 z^8 + 11741129040 z^9 + 2188432800 z^10 + 246049800 z^11 + 16770016 z^12 + 672192 z^13 + 14464 z^14 + 128 z^15) + (1/496125) (4 E^z Sqrt[Pi] (498841200 z^(9/2) + 6167491200 z^(11/2) + 17171649000 z^(13/2) + 18975733200 z^(15/2) + 10414934550 z^(17/2) + 3182619240 z^(19/2) + 575962215 z^(21/2) + 63529050 z^(23/2) + 4274760 z^(25/2) + 169840 z^(27/2) + 3632 z^(29/2) + 32 z^(31/2)) Erf[Sqrt[z]])

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]