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

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=9/2, a₂>=9/2

For fixed z and a₁=9/2, a₂=5, b₁>=-11/2

For fixed z and a₁=9/2, a₂=5, b₁=-5/2

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

Input Form

HypergeometricPFQ[{9/2, 5}, {-(5/2), -(1/2)}, z] == (1/4725) (4725 + 85050 z - 1871100 z^2 + 37837800 z^3 + 259459200 z^4 + 407927520 z^5 + 264941040 z^6 + 86616720 z^7 + 15576180 z^8 + 1592020 z^9 + 91224 z^10 + 2704 z^11 + 32 z^12) + (1/4725) (2 E^z Sqrt[Pi] (48648600 z^(7/2) + 196396200 z^(9/2) + 255446100 z^(11/2) + 151042500 z^(13/2) + 46855515 z^(15/2) + 8164905 z^(17/2) + 818160 z^(19/2) + 46280 z^(21/2) + 1360 z^(23/2) + 16 z^(25/2)) 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]