Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.ao0n)

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=1

http://functions.wolfram.com/07.25.03.ao0n.01

Input Form

HypergeometricPFQ[{6, 6}, {1, 3/2}, -z] == (1/14745600) (13852575 - 246136050 z + 755485920 z^2 - 807028320 z^3 + 391534560 z^4 - 97667520 z^5 + 13204480 z^6 - 966144 z^7 + 35584 z^8 - 512 z^9) + (1/(29491200 Sqrt[z])) ((Sqrt[Pi] (893025 - 107163000 z + 906916500 z^2 - 2082931200 z^3 + 1933437600 z^4 - 869640960 z^5 + 207657600 z^6 - 27340800 z^7 + 1967360 z^8 - 71680 z^9 + 1024 z^10) Erfi[Sqrt[z]])/E^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]