Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.af23)

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=7/2, b₁>=-11/2

For fixed z and a₁=1, a₂=7/2, b₁=-9/2

http://functions.wolfram.com/07.25.03.af23.01

Input Form

HypergeometricPFQ[{1, 7/2}, {-(9/2), 11/2}, z] == (5806080 - 1290240 z + 365568 z^2 - 73728 z^3 + 11535 z^4 - 1414 z^5 + 132 z^6 - 8 z^7)/(15 z^4) - (1/(15 z^(9/2))) (8 E^z Sqrt[Pi] (362880 - 322560 z + 141120 z^2 - 40320 z^3 + 8400 z^4 - 1344 z^5 + 168 z^6 - 16 z^7 + z^8) 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]