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

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=15/4, b_1`>=-11/2

For fixed z and a₁=15/4, b_1`=-11/2

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

Input Form

HypergeometricPFQ[{15/4}, {-(11/2), -(15/4)}, z] == (1/(8320313925 z^(1/4))) (Sqrt[2] (3 (2773437975 - 5042614500 z + 937213200 z^2 + 1053360000 z^3 + 311351040 z^4 - 86102016 z^5 + 418709504 z^6 + 30408704 z^7) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (8320313925 - 4034091600 z - 4680244800 z^2 - 1543449600 z^3 - 310464000 z^4 - 281714688 z^5 + 272498688 z^6 + 2097152 z^7) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 12 z (2773437975 + 2353220100 z + 873180000 z^2 + 222868800 z^3 + 74511360 z^4 + 41795584 z^5 + 7077888 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]