Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a84n)

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`=-1/2

http://functions.wolfram.com/07.22.03.a84n.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(1/2), 21/4}, -z] == -((221 (Sqrt[Pi] (-6005213589375 - 3112013520000 z - 1290909312000 z^2 - 751074508800 z^3 - 2145927168000 z^4 + 3051985305600 z^5 + 3487983206400 z^6 + 289910292480 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((6005213589375 - 3293547642000 z - 401762592000 z^2 + 35126784000 z^3 + 44404899840 z^4 + 202002923520 z^5 + 17867735040 z^6 + 268435456 z^7) Cos[2 Sqrt[z]] + 4 Sqrt[z] (2001737863125 + 122257674000 z + 103983264000 z^2 + 118153728000 z^3 - 156624814080 z^4 - 214711664640 z^5 - 18069061632 z^6 - 268435456 z^7) Sin[2 Sqrt[z]])))/ (692692325498880 z^(17/4)))

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]