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

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=1, a₂>=1

For fixed z and a₁=1, a₂=11/2, b₁>=-11/2

For fixed z and a₁=1, a₂=11/2, b₁=-11/2

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

Input Form

HypergeometricPFQ[{1, 11/2}, {-(11/2), -(9/2)}, z] == (1/9282994875) (9282994875 + 2062887750 z + 851350500 z^2 + 729729000 z^3 + 1654052400 z^4 + 20951330400 z^5 - 879955876800 z^6 - 8260681968000 z^7 - 15327665337600 z^8 - 11315885898240 z^9 - 4189258275840 z^10 - 866372229120 z^11 - 105336852480 z^12 - 7628759040 z^13 - 320847872 z^14 - 7176192 z^15 - 65536 z^16) - (1/9282994875) (65536 E^z Sqrt[Pi] (39916800 z^(13/2) + 199584000 z^(15/2) + 299376000 z^(17/2) + 199584000 z^(19/2) + 69854400 z^(21/2) + 13970880 z^(23/2) + 1663200 z^(25/2) + 118800 z^(27/2) + 4950 z^(29/2) + 110 z^(31/2) + z^(33/2)) 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]