Generalized hypergeometric function 2F2: Specific values (formula 07.25.03.alq2)

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=7/2, a₂>=7/2

For fixed z and a₁=7/2, a₂=6, b₁>=-11/2

For fixed z and a₁=7/2, a₂=6, b₁=-7/2

http://functions.wolfram.com/07.25.03.alq2.01

Input Form

HypergeometricPFQ[{7/2, 6}, {-(7/2), -(7/2)}, z] == (1/2480625) (2480625 + 4252500 z + 10716300 z^2 + 69854400 z^3 + 4086482400 z^4 + 189318729600 z^5 + 863493321600 z^6 + 1307011386240 z^7 + 921252021120 z^8 + 353365444320 z^9 + 80171773920 z^10 + 11251042320 z^11 + 994562864 z^12 + 55036032 z^13 + 1836032 z^14 + 33536 z^15 + 256 z^16) + (1/2480625) (8 E^z Sqrt[Pi] (3491888400 z^(9/2) + 49838770800 z^(11/2) + 160712332200 z^(13/2) + 206928981000 z^(15/2) + 133540013250 z^(17/2) + 48606365430 z^(19/2) + 10670128035 z^(21/2) + 1465368915 z^(23/2) + 127650450 z^(25/2) + 6992200 z^(27/2) + 231584 z^(29/2) + 4208 z^(31/2) + 32 z^(33/2)) 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]