Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.0990)

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=1, b₁>=-11/2

For fixed z and a₁=-11/2, a₂=1, b₁=1

http://functions.wolfram.com/07.25.03.0990.01

Input Form

HypergeometricPFQ[{-(11/2), 1}, {1, 9/2}, -z] == (1/(14155776 z^3)) ((155925 - 457380 z + 1164240 z^2 + 8030448 z^3 + 6203040 z^4 + 1757760 z^5 + 221952 z^6 + 12544 z^7 + 256 z^8)/E^z) + (1/(28311552 z^(7/2))) (Sqrt[Pi] (-155925 + 561330 z - 1496880 z^2 + 6985440 z^3 + 20956320 z^4 + 13970880 z^5 + 3725568 z^6 + 456192 z^7 + 25344 z^8 + 512 z^9) 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]