Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.am0p)

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=4, a₂>=4

For fixed z and a₁=4, a₂=9/2, b₁>=-11/2

For fixed z and a₁=4, a₂=9/2, b₁=-7/2

http://functions.wolfram.com/07.25.03.am0p.01

Input Form

HypergeometricPFQ[{4, 9/2}, {-(7/2), 3/2}, z] == (1/33075) (33075 - 113400 z + 249480 z^2 - 617760 z^3 + 3603600 z^4 + 6289920 z^5 + 3158400 z^6 + 687744 z^7 + 71952 z^8 + 3520 z^9 + 64 z^10) + (1/33075) (8 E^z Sqrt[Pi] z^(9/2) (720720 + 950040 z + 433800 z^2 + 90255 z^3 + 9210 z^4 + 444 z^5 + 8 z^6) 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]