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

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=6, a₂>=6

For fixed z and a₁=6, a₂=6, b₁>=-11/2

For fixed z and a₁=6, a₂=6, b₁=-3/2

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

Input Form

HypergeometricPFQ[{6, 6}, {-(3/2), 2}, z] == (1/2764800) (2764800 - 33177600 z + 541900800 z^2 + 3171494025 z^3 + 4509070740 z^4 + 2718095040 z^5 + 837480720 z^6 + 143376480 z^7 + 14051520 z^8 + 776192 z^9 + 22272 z^10 + 256 z^11) + (1/5529600) (E^z Sqrt[Pi] (2608781175 z^(5/2) + 9358484850 z^(7/2) + 11156230800 z^(9/2) + 6159160800 z^(11/2) + 1806032160 z^(13/2) + 300081600 z^(15/2) + 28857600 z^(17/2) + 1574400 z^(19/2) + 44800 z^(21/2) + 512 z^(23/2)) 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]