Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agcr)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.agcr.01

Input Form

HypergeometricPFQ[{23/4}, {-(11/2), -(21/4)}, -z] == (1 - (508 z)/231 + (1440 z^2)/1309 - (178624 z^3)/595595 + (19456 z^4)/292383 - (32768 z^5)/1686825 + (524288 z^6)/9398025 - (8107589632 z^7)/635218148565 + (67108864 z^8)/756212081625) Cos[2 Sqrt[z]] - (1/142924083427125) (2 Sqrt[z] (-142924083427125 + 123743795175000 z - 43053135325200 z^2 + 10098730857600 z^3 - 2335931136000 z^4 + 996663951360 z^5 + 3340763136000 z^6 - 111962750976 z^7 + 134217728 z^8) Sin[2 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,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},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]