Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ajs2)

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=-9/2

http://functions.wolfram.com/07.25.03.ajs2.01

Input Form

HypergeometricPFQ[{5/2, 6}, {-(9/2), -(9/2)}, z] == (1/40186125) (40186125 + 29767500 z + 29767500 z^2 + 57153600 z^3 + 314344800 z^4 + 16345929600 z^5 + 685703491200 z^6 + 2874036211200 z^7 + 4043596999680 z^8 + 2671074282240 z^9 + 966119353920 z^10 + 207696767040 z^11 + 27727388640 z^12 + 2339264928 z^13 + 123890304 z^14 + 3965184 z^15 + 69632 z^16 + 512 z^17) + (1/40186125) (16 E^z Sqrt[Pi] (6666332400 z^(11/2) + 87687910800 z^(13/2) + 262807335000 z^(15/2) + 316640734200 z^(17/2) + 192275625150 z^(19/2) + 66158385930 z^(21/2) + 13783051485 z^(23/2) + 1802482605 z^(25/2) + 149957010 z^(27/2) + 7864920 z^(29/2) + 249984 z^(31/2) + 4368 z^(33/2) + 32 z^(35/2)) 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]