Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0548)

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=-11/2, a₂>=-11/2

For fixed z and a₁=-11/2, a₂=-3/2, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=-3/2, b₁=-5/2

http://functions.wolfram.com/07.25.03.0548.01

Input Form

HypergeometricPFQ[{-(11/2), -(3/2)}, {-(5/2), 11/2}, -z] == (1/(157286400 z^4)) ((-7640325 + 13617450 z - 17629920 z^2 + 25613280 z^3 + 72927840 z^4 + 22952640 z^5 + 245760 z^6 - 543232 z^7 - 55552 z^8 - 1536 z^9)/E^z) + (1/(314572800 z^(9/2))) (Sqrt[Pi] (7640325 - 18711000 z + 28066500 z^2 - 39916800 z^3 + 104781600 z^4 + 167650560 z^5 + 46569600 z^6 - 1140480 z^8 - 112640 z^9 - 3072 z^10) 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]