Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.1218)

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=1/2

http://functions.wolfram.com/07.25.03.1218.01

Input Form

HypergeometricPFQ[{-(11/2), 3/2}, {1/2, 11/2}, -z] == (1/(7864320 z^4)) ((1091475 - 1611225 z + 1538460 z^2 - 1164240 z^3 + 6789840 z^4 + 10013280 z^5 + 3731520 z^6 + 553216 z^7 + 34816 z^8 + 768 z^9)/E^z) + (1/(15728640 z^(9/2))) (Sqrt[Pi] (-1091475 + 2338875 z - 2806650 z^2 + 2494800 z^3 + 20956320 z^5 + 23284800 z^6 + 7983360 z^7 + 1140480 z^8 + 70400 z^9 + 1536 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]